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Repositories

Latest version of each Zenodo concept by Logica Artificialis. A row shows only the files on that record, and a GitHub address only when the manuscript names one.

146 repositories

• 10.5281/zenodo.238380122026

  Order extension in Chehata's group

  Martino Lupini · Orderability, Groups

  In the real case, Chehata's group consists of the increasing piecewise-linear homeomorphisms of the real line with finitely many pieces and bounded support. We prove that every bi-invariant partial order on this group extends to a bi-invariant total order, answering the real-field form of the question recorded in the 2009 survey of Bludov, Glass, Kopytov, and Medvedev. More precisely, a set of nonidentity elements generates a normal semigroup containing the identity if and only if the logarithms of its initial slopes and those of its final slopes each admit a nonempty positive integer relation. Every partial order therefore extends to an endpoint-slope order induced by an additive total order on the abstract group of real numbers. These orders form two disjoint families and exhaust all bi-orders; their number is 2^{2^{aleph_0}}. The proof creates an arbitrary endpoint germ after cancellation of a positive germ relation and then applies an equal-germ positive factorization argument. Over an Archimedean ordered field F, the analogous criterion and classification use additive orders on the logarithmic slope group and give 2^{|F|} bi-orders.

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• 10.5281/zenodo.238353112026

  Groups with prescribed finite numbers of lattice orders

  Martino Lupini · Orderability, Groups

  We prove that the possible finite numbers of lattice group orders on an ℓ-orderable group are exactly 1 and the positive even integers. We also construct, for every n ≥ 1, a countable nonabelian simple group with exactly 2n bi-invariant total orders. These results answer the finite-spectrum questions in the 2009 problem list of Bludov, Glass, Kopytov, and Medvedev. The lattice-order construction rests on a classification of all lattice orders on certain groups of homeomorphisms of the line. For the complementary examples, we show that every lattice order on the affine family used here, due to Kopytov, is total.

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• 10.5281/zenodo.238333062026

  Finite configurations and nuclear quotients of Thompson's group F

  Martino Lupini · Thompson groups, C*-algebras, Operator algebras

  Let F be Thompson’s group, let P = F′, and let Ug denote the canonical prefix-table unitaries in the Cuntz algebra O₂. We prove that the finite ordinary tensor images Bn = C*(Uf⊗n : f ∈ F) and Cn = C*(Up⊗n : p ∈ P) are nuclear. A representation has finite separated derived capacity when products of sufficiently many displacement operators with separated interior supports vanish. Capacity at most d gives an actual marked quotient of B2d+2, or of C2d for a nontrivial P-representation. Infinite capacity is equivalent to admitting the regular representation as an actual quotient. Consequently, if F is nonamenable, every nonzero nuclear quotient of its full group C*-algebra, and likewise of C*(P), is a quotient of one of these finite canonical images. The finite nuclearity and norm estimates are unconditional; nonamenability enters only in passing from nuclearity to finite capacity. The result gives a countable cofinal family of nuclear quotients, with a degree depending on the quotient.

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• 10.5281/zenodo.238320582026

  Charmenability of Thompson's group F

  Martino Lupini · Thompson groups, C*-algebras, Amenability

  We prove that Thompson's group F and its commutator subgroup F′ are charmenable. The main assertion is that every nonempty compact convex conjugation-invariant family of normalized positive-definite functions on either group contains a trace. Its proof uses commuting groups supported on disjoint intervals and a stationary averaging argument on their joint von Neumann algebra. It is independent of nonamenability of F. The character condition in charmenability follows from the classification of finite factor representations by Dudko and Medynets. We also prove that F is not charfinite and that F′ is charfinite precisely when F is nonamenable. Every nonzero simple quotient of either full group C*-algebra is scalar or is the corresponding reduced group algebra, and every nonzero nuclear quotient admits a multiplicative character.https://github.com/eulogica/charmenability-of-thompsons-group-f

  No files · GitHub named

• 10.5281/zenodo.238280862026

  Normal-semigroup generators for the bi-order cones of Thompson's group F′

  Martino Lupini · Thompson groups, Orderability, Groups

  The commutator subgroup F′ of Thompson's group has four bi-invariant total orders, determined by the slope at the first or last point of support. We prove that the positive cone of each order is generated by two elements as a normal semigroup: every positive element is a nonempty product of conjugates of those two elements. An explicit pair f, g works for all four cones, using the four choices of signs (f, g), (f⁻¹, g⁻¹), (f⁻¹, g), and (f, g⁻¹). This answers the finite-generation question posed by Navas and Rivas in 2008, including their stronger requirement that the same pair yield both prescribed partitions of F′\{1}. Two generators are necessary for each cone.

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• 10.5281/zenodo.238276522026

  Failure of rational injectivity for minimal principal étale groupoids

  Martino Lupini · Orderability, Groupoids, Groups

  Applying OpenAI's torsion-free group counterexample, we construct a second-countable locally compact Hausdorff minimal principal ample groupoid with Cantor unit space whose ordinary reduced Baum--Connes assembly map has an infinite-order kernel class in degree zero. Its rationalization is therefore not injective, with the natural coefficient algebra of continuous functions on the unit space. The groupoid is a transformation groupoid of a finitely generated torsion-free group and is compactly generated. We use the invariant-measure trace class of Antonini, Azzali and Skandalis to preserve an ordinary assembly kernel class under extension of coefficients to continuous functions. Elek's free minimal measure-preserving Cantor action supplies the required dynamics. The standard compact-action comparison identifies group assembly with coefficients and transformation-groupoid assembly. Thus minimality and principality do not restore the natural-coefficient reduced Baum--Connes assertion.

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• 10.5281/zenodo.238040062026

  Order-universal free subgroups and bi-order extension

  Martino Lupini · Orderability, Groups

  We construct fixed free subgroups along which every prescribed bi-order extends to the ambient group. Such subgroups exist inside every nontrivial normal subgroup of a free group of rank two. A finite-support localization theorem transfers this property to other bi-orderable groups, using one visible element and an invariant order on the actual intermediate quotient. We apply it to every bi-orderable rank-two free-by-cyclic group, to higher-rank monodromies with positive real homology spectrum not entirely equal to one, and to an explicit IA mapping torus. The last example and all its height cyclic covers admit no compatible cyclic-cover free quotient in any integral character direction, but still have the required universal free subgroups. Consequently total Bi-order Extension is undecidable in each of these fixed groups, already for a fixed finite background and one varying word. The argument also distinguishes the order-transfer problem from the existence of free quotients in finite covers.

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• 10.5281/zenodo.237601692026

  Finite incidence models for elliptic resonance varieties

  Martino Lupini · Mathematics

  Let E = A ⊕ B be a sum of line bundles of degrees 2 ≤ a ≤ b on a smooth complex elliptic curve. We determine all irreducible components of the locus of two-dimensional spaces of sections that generate a sheaf of rank one. Their number is a if A ≇ B, and max{1, a−2} if A ≅ B. Relative Grassmannians and projective bundles give smooth finite normalization models for these components. In saturation degree two, the normalization maps are closed embeddings.

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• 10.5281/zenodo.237317872026

  A finitely presented nonindicable subgroup of a free profinite group

  Martino Lupini · Groups

  We construct an infinite, two-generated, finitely presented subgroup H of the free profinite group of rank two whose abelianization is (ℤ/60ℤ)^2. Thus free profinite groups of rank at least two fail to be locally indicable, disproving a conjecture of Jaikin-Zapirain. The group H has a normal subgroup of index 60 isomorphic to F_29 × F_19 × F_11, where F_r denotes the abstract free group of rank r. More generally, every nontrivial finite perfect group is a quotient of a finitely presented torsion-free group with finite abelianization that embeds in the free profinite group of rank two. The construction combines free products of finite cyclic groups over a common finite quotient, completing a different free kernel at each prime.

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• 10.5281/zenodo.236830422026

  Nonmeagre ideals from traces on corona algebras

  Martino Lupini · C*-algebras

  We show that a tracial state on the corona of a separable nonunital C*-algebra gives a proper nonmeagre ideal in its multiplier algebra. Here nonmeagreness is the block condition introduced by Vignati and Yilmaz: every good approximate identity and every disjoint sequence of finite intervals admit an infinite block sum in the ideal. More generally, an ideal containing the original algebra is nonmeagre whenever its quotient has only countable families of pairwise orthogonal nonzero positive elements. Applying this criterion to Goodearl's simple AF example answers Question 4.13 of Vignati and Yilmaz affirmatively in ZFC. Goodearl's examples also yield a simple AF algebra with uncountably many maximal proper nonmeagre multiplier ideals.

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• 10.5281/zenodo.236828572026

  Local units and multiplier algebras of AF corona ideals

  Martino Lupini · Mathematics

  Let A be a simple unital separable infinite-dimensional AF algebra, fix a tracial state τ, and put D = A ⊗ K. Let I be the closed trace ideal of M(D) associated with τ, and set J = I/D and Q = M(D)/D. We prove that, under the Continuum Hypothesis, the canonical inclusion Q ⊂ M(J) is proper. More precisely, there is a positive contraction m ∈ M(J) such that dist(m,Q) = 1/2 and |M(J)| = dens‖·‖ M(J) = 2^c, where c = 2^ℵ₀. The construction produces globally compatible multiplier actions on an exhaustive family of projection corners. Countable Riesz separation suffices for the limit-stage interpolation. In ZFC, every countable subset of J has a projection unit, with a lift of arbitrarily small finite trace, and every multiplier agrees on that subset on both sides with an element of J.

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• 10.5281/zenodo.236826802026

  Jordan spectra of nilpotent derivations from scalar geometry

  Martino Lupini · Orderability, Groups

  We determine the complete Jordan spectrum of nilpotent derivations of a nonabelian class-two Lie algebra I over a characteristic-zero field. We assume that its scalar bracket space has a decomposable basis over the ground field and that its reduced geometric decomposable locus admits no nontrivial additive-group action. A plane-preserver algebra and a hyperplane arrangement determine the horizontal rank set R; an integer criterion then decides every full Jordan type. Every admitted type occurs over the ground field, and the spectrum remains unchanged under field extension. For u = dim(I/Z(I)), d = dim I′, f = dim(Z(I)/I′), and r = max R, the greatest partition is (2^r, 1^(u-2r)) + (f) + (1^d), with componentwise addition. The full spectrum recovers R and is a dominance order ideal exactly when R has no gaps. For fixed free central dimension f, finite scalar loci with identical support-sum rank functions can have different spectra; support dimension six is minimal. A family has Jordan strata and commuting varieties whose component dimensions differ without bound. Geometric consequences include a smooth rational greatest-type stratum, a crepant resolution, and a classification of nilpotent linear spaces of largest dimension. Hall polynomials give uniform Jordan-stratum point counts at almost all places for number-field models.

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• 10.5281/zenodo.236824122026

  The noncommutative weak extension principle under OCA

  Martino Lupini · C*-algebras, Descriptive set theory

  We prove that the Open Colouring Axiom implies the noncommutative weak extension principle. Every *-homomorphism between coronas of separable nonunital C*-algebras therefore splits, by a commuting projection, into a part with Borel graph and a part with nonmeagre kernel. This removes Martin's Axiom from Vignati and Yilmaz's theorem and answers their proposed weakening for Theorem A. In particular, all such homomorphisms with stable source are Borel under the Open Colouring Axiom alone. We also obtain Borel product lifts for bounded linear maps between reduced products of separable Banach spaces and separable C*-algebras which respect the canonical coordinate restrictions.

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• 10.5281/zenodo.236405402026

  Positive normal identities and bi-order extension

  Martino Lupini · Orderability, Groups

  We prove that it is undecidable whether the identity in a free group of any fixed finite rank at least two is a nonempty product of conjugates of given elements, with only positive occurrences of those elements allowed. It is also undecidable whether a finite subset of that group can be made positive in a total order invariant under multiplication on both sides. Both conclusions hold for a fixed finite background together with one varying word, all lying in the commutator subgroup. These give negative answers to the normal identity and bi-order questions stated online in 2025 by Bodart, Ciobanu and Metcalfe, and to the bi-order extension question formulated by Colacito and Metcalfe (2017). The second result also settles their 2019 question about the word problem for free representable lattice-ordered groups: it is undecidable already on two generators.

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• 10.5281/zenodo.235230912026

  Simple left-orderable groups with prescribed finiteness length

  Martino Lupini · Orderability, Groups

  For every integer n ≥ 2 we construct an infinite simple left-orderable group of type F_n and not of type FP_{n+1}(ℤ), and hence not of type F_{n+1}, where type F_n means that a classifying space has finite n-skeleton. This answers affirmatively the left-orderable interpretation of a question of Xiaolei Wu in the problem list associated with the 2024 CIRM meeting. The construction inserts arithmetic groups of one-sided germs into a group of homeomorphisms of the line. A forest complex controls the finiteness of the germ groups, and an actual interval-lift argument controls the singularity stabilizers. An (n−1)-connected band in the germ complex then gives type F_n for the simple derived subgroup. A Lipschitz retraction onto a kernel of endpoint characters retains the homological finiteness obstruction.

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• 10.5281/zenodo.235206832026

  Semiprojectivity and norm-controlled lifting in Banach lattices

  Martino Lupini · Orderability

  We characterize semiprojectivity of a real Banach lattice by almost contractive lifting through ideal quotients of separable Banach lattices, with no separability assumption on the domain. Semiprojectivity is equivalent to ℓ-openness, implies ℓ-closedness, and is unchanged if the finite ideal stage is allowed to depend on the norm tolerance. For separable domains it coincides with 1⁺-projectivity. We prove that arbitrary ℓ₁-sums preserve semiprojectivity without an order-unit hypothesis on the summands. In contrast, ℓ₁(ℕ) ⊕∞ ℝ is not semiprojective, although both summands are 1⁺-projective. Thus semiprojectivity need not pass to finite ℓ∞-sums or split extensions. The example is ∞-projective with infimum of uniform projectivity constants equal to 2, admits an equivalent 1⁺-projective lattice norm, and is not ℓ-closed.

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• 10.5281/zenodo.234770162026

  Ascending chains of sublattices in free lattices

  Martino Lupini · Mathematics

  We prove that every increasing sequence of free sublattices of bounded finite rank in a free lattice is eventually constant. In particular, there is no infinite strictly increasing chain of copies of the free lattice on three generators, answering negatively a question of R. A. Dean recorded in 1997. Freeness is essential: we construct in the three-generated free lattice an infinite strictly increasing chain of pairwise nonisomorphic retracts, each requiring exactly three generators. The corresponding retractions commute. We also give a proper self-embedding whose fixed-point sublattice contains a free copy of the ambient lattice, and prove that the stable image of every endomorphism of a finitely generated free lattice consists precisely of its periodic points.

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• 10.5281/zenodo.234699552026

  Order, norming faces, and symmetries of Tursi's Banach lattice

  Martino Lupini · Orderability, Groups

  Let L be Tursi’s separable universal homogeneous real Banach lattice. The set of decreasing positive sequences with infimum zero is coanalytic complete, even for sequences of components of one fixed quasi-interior vector, providing a fixed-lattice coanalytic-complete example for the decreasing-order-complexity question raised in Tursi’s 2024 survey. This gives a negative answer to the 2024 question of Avilés, Rosendal, Taylor, and Tradacete whether every separable Banach lattice belongs to their countable Fatou hierarchy. Unrestricted sequential order convergence has the exact complete complexity coA(Pi^1_1), the dual of one Souslin operation on coanalytic sets. We classify quasi-interior positive vectors by their norming Choquet simplices and answer Tursi’s documented 2021 automorphism-group universality question affirmatively. We prove universality of embedding orbits for every nonzero separable domain and of automorphism conjugacy, and establish concentration, lifting, and representation results for pointwise face kernels. Further results describe generic embedding orbits, ideals, and finite-dimensional approximate disposition.

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• 10.5281/zenodo.234696252026

  Forests as Heyting spectra: representation criteria, constructions, and obstructions

  Martino Lupini · Orderability

  Our main result shows that an Esakia space whose order is a downward forest has a locally finite clopen-upset algebra whenever its maximal boundary is scattered. More precisely, failure of local finiteness forces a nonempty perfect principal maximal boundary. We also construct locally finite representations of immediately splitting trees without assuming well-foundedness, and classify the cardinal multiplicities of a uniform family of binary canopies. The countable-forest inverse-sequence characterization and failure of infinitary order axiomatizability are consequences of these results, using established inverse-limit and model-theoretic methods. We give finite-partition certificates as explicit forms of the existing duality and compactification machinery. The unrestricted intrinsic structural classification of forest spectra remains unresolved here.

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• 10.5281/zenodo.234611402026

  Endomorphism counts from primitive orbits and synchronized block actions

  Martino Lupini · Orderability, Posets, Groups

  For a finite poset P, let R(P) = |End(P)|/|Aut(P)|, where endomorphisms preserve the reflexive order. We prove R(P) ≥ 2^{|P|/(64 log₂ |P|)} for |P| ≥ 4 when every chain has at most two elements and the action on each nonsingleton automorphism orbit is primitive. The same bound holds for a class of imprimitive actions: on each interaction component the action must be the full automorphism group of a rooted tree, acting identically on all the identified orbits. The proof combines simultaneous collapses of indices with maps into principal ideals and filters. We give counting lemmas that retain the whole kernel of a block action, and a quantitative collapse, degree, or orbit-size alternative for normal products of alternating groups with natural orbits. We also construct connected twin-free posets with group S₃ wr Sₜ, constant minimum of the two maximum principal-set sizes, and imprimitive action on every orbit, although every orbit-preserving endomorphism is an automorphism. A restricted three-level extension has lower bound 2^{|P|/(128 (log₂ |P|)²)}. These results give partial answers to the finite-poset automorphism problem of Rival and Rutkowski; the unrestricted question remains beyond the arguments here.

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• 10.5281/zenodo.234584502026

  A countable scattered poset without a strongly maximal chain

  Martino Lupini · Orderability, Posets

  A chain C in a partially ordered set is strongly maximal if |D \ C| ≤ |C \ D| for every chain D. We construct a countably infinite poset with no infinite antichain and no strongly maximal chain. The poset is scattered: none of its chains contains a copy of the rational order. This gives a negative answer, already in the countable scattered case, to the strong-chain question posed by Hollom in 2024 and restated in 2026. The construction replaces each point (x, y, n) of Hollom’s layered poset by a finite chain of length 2^x + 2^y. A finite path exchange restricts the possible chains, after which a further finite exchange always improves them. We also analyze a width-two example of Hollom showing that the chain-extension inclusion used in an earlier claimed positive proof need not hold.

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• 10.5281/zenodo.234527882026

  The small index property for the random poset

  Martino Lupini · Posets, Descriptive set theory, Groups

  Let P be the countable universal homogeneous poset. We prove that every abstract subgroup H ≤ Aut(P) with [Aut(P):H] < 2^{ℵ₀} contains the pointwise stabilizer of a finite subset of P. Thus Aut(P) has the small index property, answering the question recorded as open by Barbina and Macpherson in 2005. No regularity assumption on H is required. The proof equips P with a generic strictly increasing rational-valued rank. Its stabilizer has ample generics, and generic pairs of ranks yield a comeager double coset. We show that the small index property passes from a closed subgroup with such a double coset to the ambient Polish group.

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• 10.5281/zenodo.234517182026

  Simultaneous avoidance of power families of null sequences

  Martino Lupini · Mathematics

  Let (a_n) be a positive sequence tending to zero with liminf a_(n+1)/a_n > 0. For every η ∈ (0,1), we construct a compact set E ⊆ [0,1] of Lebesgue measure greater than 1−η such that {x+s a_n^λ : n ≥ 1} is not contained in E for any x ∈ ℝ, s ≠ 0, and λ > 0. No monotonicity is required, and one set works for all positive powers simultaneously, with infinitely many distinct points of every copy outside E. Taking a_n=e^(−n) gives one compact set of measure arbitrarily close to one containing no infinite geometric progression of any ratio in (0,1), answering negatively a question of Burgin, Goldberg, Keleti, MacMahon and Wang. We also prove a uniform finite hitting statement for ratios in a compact range and scales in [1,2]. The proof adapts random routing to grids shared by all exponents, with a localized count of exponent and scale parameters and a compactness repair for exceptional centres.

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• 10.5281/zenodo.234405222026

  A countable norm construction for free Banach lattices under arbitrary convexity implications

  Martino Lupini · Orderability

  We give an explicit countable construction of the norm of the free Banach lattice of an arbitrary prescribed convexity type over a pre-ordered Banach space. Starting with the ordinary free Banach lattice, each step takes the gauge of a closed solid absolutely convex hull determined by the original convexity implications. If $p_k$ is the seminorm obtained after $k$ steps, then the free norm is $p_\omega=\inf_{k<\omega}p_k$. No continuity is required of the increasing numerical functions in the implications, and every antecedent is retained in full. The proof uses disjoint cutoffs that repair the antecedents while preserving the value of one positive functional. The same estimate gives quotient closure and an exact restriction of each successor gauge to finite-dimensional vector sublattices. Applying classical compactness to the resulting class yields a local norm formula over finite-dimensional linear input spaces and finite sets of complete implications. Consequently every strict decrease of the free norm is witnessed at a finite input dimension, a finite set of implications, and a finite stage. For each fixed separable input, a countable subfamily of complete conditions already determines the same free norm. For one presentation of the AM-space type, no finite stage computes the norm on all lattice expressions. The formula also gives an intrinsic isometry criterion, without providing the convenient geometric test asked for by de Jeu and Jiang.

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• 10.5281/zenodo.234405102026

  Geometric criteria for the sequential Dini property

  Martino Lupini · Operator algebras

  Let $C$ be a closed pointed convex cone in a real Banach space $X$, and set $$q_C(x)=\max\{\operatorname{dist}(x,C),\operatorname{dist}(x,-C)\}.$$ We prove that every increasing weakly convergent sequence converges in norm if and only if every weakly null sequence $(x_n)$ satisfying $q_C(x_n)\to0$ is norm null. Equivalent conditions are a sandwich principle on relatively weakly compact sets and uniform equivalence of the $q_C$ and norm metrics on each weakly compact subset, with a modulus depending on the weakly compact set. These give intrinsic geometric criteria for the property in a characterization question posed by Jochen Glück in 2024. They distinguish the sequential property from normality, which requires a uniform lower bound for $q_C$ on the entire unit sphere. Rosenthal's theorem yields an equivalent criterion through $\ell^1$ basic sequences. In particular, on a space containing no copy of $\ell^1$, the property is equivalent to normality. A closed nonnormal cone with the property exists on a Banach space exactly when it contains $\ell^1$, with no generating requirement on the cone. The criteria also show failure of the property for the pointwise cones of $C^k[-1,1]$, $k\geq1$, and $W^{1,1}(-1,1)$.

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• 10.5281/zenodo.234404832026

  Peripheral eigenspace dimensions for positive operators and semigroups

  Martino Lupini · Orderability, Operator algebras

  Let $T$ be a positive contraction on a monotonically complete complex Banach lattice with the Fatou property. We prove $$\dim\ker(\lambda I-T)\leq\dim\ker(\lambda^k I-T) \qquad (|\lambda|=1,\ k\in\mathbb Z),$$ where all infinite dimensions are identified with infinity. This answers an open problem posed by Jochen Glück in 2021 and extends the previously established root-of-unity case. The bounded bilateral trajectories of $T$ form an intrinsic Banach lattice by the fixed-space theorem. On this lattice, the shift is a lattice automorphism, and evaluation at zero identifies its unimodular eigenspaces with those of $T$. We also prove the corresponding multiplicity inequality for imaginary generator eigenspaces of positive contractive $C_0$-semigroups, and for positive power-bounded operators that are order continuous.

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• 10.5281/zenodo.234404152026

  Lipschitz positive decompositions of von Neumann preduals

  Martino Lupini · Mathematics

  We prove that the selfadjoint predual of a complex von Neumann algebra admits a Lipschitz positive decomposition if and only if the algebra is subhomogeneous. In particular, infinite-dimensional selfadjoint trace class gives a negative answer to the Lipschitz decomposition problem, confirming Messerschmidt's 2018 conjecture. For a nonzero subhomogeneous algebra of maximal matrix degree $d$, the least Lipschitz constant of a positive majorant $q(x)\geq\pm x$ is attained and equals the corresponding constant $c_d$ for $d\times d$ trace class. Among nonzero von Neumann algebras, the optimal constant equals one exactly for the abelian algebras. The finite-dimensional constants satisfy $$c\log\log N\leq c_N\leq C\log N$$ for all sufficiently large $N$, with absolute constants $c,C>0$. The lower bound applies to arbitrary positive majorants; the upper bound comes from the classical absolute-value estimate.

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• 10.5281/zenodo.234403022026

  Isometric canonical maps into free convex Banach lattices

  Martino Lupini · Mathematics

  For every $1<p<\infty$, we construct a three-dimensional real Banach lattice $X$ which is not $p$-convex with constant one, although its canonical positive map into the free $p$-convex Banach lattice with constant one is isometric. Dimension three is minimal. In every dimension $n\geq3$, such examples can be arbitrarily close to $\ell_p^n$ under the coordinate lattice isomorphism. An elementary example answers the necessity question raised by Marcel de Jeu and Xingni Jiang in 2025 for general convexity types; the three-dimensional construction gives a negative answer even for ordinary constant-one $p$-convexity. We characterize isometry by an exact factorization of dual functionals through two positive coordinates. For a Banach lattice, the criterion says that every sublattice of $X^*$ generated by two disjoint positive elements is $p'$-concave with constant one. The counterexample separates this two-generator condition from full concavity. At $p=\infty$, in contrast, isometry forces the original norm to be an AM-space norm.

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• 10.5281/zenodo.234401542026

  Common null complements for polynomial images of finite sums of perfect sets

  Martino Lupini · Mathematics

  Fix an integer D ≥ 1, and let A₁, …, A₍D₊₂₎ be nonempty compact perfect subsets of the real line. For their Minkowski sum C = A₁ + ⋯ + A₍D₊₂₎, we construct a single null Fσ set B ⊆ ℝ such that P(C) + B = ℝ for every nonconstant real polynomial P of degree at most D. In particular, every sum of three compact perfect sets has one null complement that works under every nonzero dilation. Thus the conclusion of Jung and Lai’s Conjecture 4.8 holds for these sums; the conjecture remains open for arbitrary perfect sets. The conclusion applies to some sums with zero logarithmic Hausdorff and packing dimensions that contain no polynomial image of an infinite summable finite-digit product. The proof isolates a local sum hypothesis that permits the same construction for more general compact sets.

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• 10.5281/zenodo.234399852026

  Critical ideals and covering widths of ideal Schauder bases

  Martino Lupini · Descriptive set theory

  An ideal Schauder basis of a Banach space expands every vector as a series whose partial sums Sₙx converge along an ideal of subsets of ℕ, rather than along the cofinite sets. Its critical ideal is the least ideal with this property: it is generated by the finite sets and the error sets {n: ‖x − Sₙx‖ ≥ ε}. We determine the possible descriptive complexities of critical ideals and study when they are P-ideals. If the coordinate functionals are continuous, the critical ideal is complete for exactly one of the classes Fσ, Fσδ and Fσδσ, and all three cases occur; it is Fσ if and only if it is a P⁺-ideal, and it is always Fσ in a reflexive space. Since analyticity of a critical ideal forces continuity of the coordinates, an analytic critical ideal is Borel. A critical ideal need not be a P-ideal, even for a basis of a separable Hilbert space; the P-property is equivalent to a uniform bound on the number of vectors whose error sets are needed to cover a member of the ideal. Every proper analytic P-ideal is isomorphic to the critical ideal of a basis of ℓ₁ ⊕ c₀, but there is a pathological Fσ P-ideal on ℕ that is not the critical ideal of any basis of any Banach space. These results answer Questions 11.3 and 11.4 of Kwela and Swaczyna (2025) negatively, and their Question 11.2 negatively as stated and positively up to isomorphism. Elementary coordinatewise examples also illustrate a negative answer to their Question 11.1; the dense-span ℓ₁ existence phenomenon is already implicit in classical non-strong Markushevich basis constructions. We also show that every proper nonpathological Fσ P-ideal I is the critical ideal of a basis of a reflexive space and satisfies I = Fin(ψ) = Exh(ψ) for a nonpathological lower semicontinuous submeasure ψ; this answers a question of Lopez-Abad, Olmos-Prieto and Uzcátegui-Aylwin (2025).

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• 10.5281/zenodo.234388512026

  Universal minimal flows from pointwise completions and atomic decomposition

  Martino Lupini · Orderability, Operator algebras, Descriptive set theory

  We organize explicit universal minimal flows of mapping and transformation groups around two standard reductions: passage to a compact group completion and removal of a closed extremely amenable normal subgroup. Finite interpolation identifies the pointwise completions of path, loop, gauge, and section groups; for disconnected compact Lie targets the completion also records the clopen information in the source. For measurable maps into a compact metrizable group K, the established atomless fixed-point theorem gives M(L0(Y, μ; K)) = KAμ, where Aμ is the set of atoms. Combining these reductions with known structure and compact-extension theorems yields atomic formulas for measure-space transformations, Lp-isometries, and automorphism groups of operator algebras. The general Banach-valued statement uses complex fibres; real Hilbert fibres are treated separately. We also give the formula M(FΩ ⋊ Sym(Ω)) = M(F)Ω × LO(Ω) for a Polish group F with metrizable universal minimal flow and a countable set Ω, with the natural skew action. Its ordered relational special cases have earlier Ramsey-theoretic treatments. The results are presented as explicit consequences and extensions of the cited completion, extreme-amenability, and structural results.

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• 10.5281/zenodo.234376442026

  Spectral criteria for extending partial left orders

  Martino Lupini · Orderability, Groups

  We answer affirmatively two extension questions posed by Bodart, Ciobanu, and Metcalfe in 2024: every partial left order extends to a total left order on the group of positive rational affine transformations, and on every group ℤ² ⋊T ℤ with T ∈ SL₂(ℤ) and tr(T) > 2. Both follow from a metabelian criterion: it suffices that the group be torsion-free, its derived subgroup have finite rational rank, and all conjugation eigenvalues on that subgroup be positive real. We derive more general extension results from structural theorems of Dong and Bodart–Dong. For groups with a finite-rank nilpotent normal subgroup and abelian quotient, extension of arbitrary partial left orders is equivalent to extension of total left orders from subgroups. This connects the cyclic case with Pierce’s classical theorem. A unified spectral criterion allows a locally nilpotent derived subgroup: under local finiteness and positive spectrum modulo its center, full extension is equivalent to the requirement that a central eigenvalue whose positive power is positive real is itself positive real. The proofs explain how local affine certificates yield orders on the prescribed ambient group.

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• 10.5281/zenodo.234301632026

  Completely positive coordinates for KK-theory and relative uniform stability

  Martino Lupini · C*-algebras, Amenability, Groups

  Let A be a unital nuclear C*-algebra, M a von Neumann algebra, and I a norm-closed ideal of M. We prove that a unital completely positive map Φ:A→M, multiplicative modulo I, admits a unital homomorphic correction with the same quotient map whenever

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• 10.5281/zenodo.234257012026

  Pairwise mixing layouts and self-joinings of weakly mixing transformations

  Martino Lupini · Orderability

  Let T be an invertible weakly mixing transformation of a standard probability space (X, μ). We prove that pairwise mixing along any prescribed finite family of integer sequences implies joint mixing: if every two-coordinate marginal of (T^{d₁(b)}x, …, T^{dₖ(b)}x), for x distributed according to μ, converges to μ², then the full distribution converges to μᵏ. No entropy assumption is needed. This answers Ryzhikov's question on mixing sequences. The proof depends essentially on structural results from OpenAI's multiple-mixing preprint. For weakly mixing rank-one transformations, a tower argument shows that every pairwise-independent finite self-joining is product, answering the corresponding questions in Ryzhikov's problem list. Finally, for invertible ergodic transformations of standard nonatomic spaces, two-fold minimal self-joinings imply minimal self-joinings of all finite orders. This follows from OpenAI's theorem and Ryzhikov's equivalence with the restricted multiple-mixing problem.

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• 10.5281/zenodo.234249602026

  Robust fixed points and finite classifying spaces: CAT(0) actions, Banach targets and group fillings

  Martino Lupini · Groups

  For a finitely presented group, we characterize the fixed-point property for all isometric actions on complete CAT(0) spaces by finite systems of polynomial distance inequalities. An infeasible system gives a uniform tolerance for simultaneous errors in the generating maps, defining relations and midpoint geometry. For finite presentations, this yields an algorithm that halts exactly when the property holds. On genuine CAT(0) spaces and prescribed Banach classes, continuous iterations give locally Hölder retractions onto common fixed sets and continuous choices in parameter families. For one arithmetic presentation we evaluate a nonlinear generator tolerance of 10−232 on genuine CAT(0) spaces.

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• 10.5281/zenodo.234220762026

  Isomorphism is strictly Borel reducible to quasi-isometry for finitely generated groups

  Martino Lupini · Descriptive set theory, Groups

  We prove that isomorphism of finitely generated groups is strictly Borel reducible to quasi-isometry, confirming a conjecture of Simon Thomas. More precisely, we construct continuous reductions to quasi-isometry of both the universal countable Borel equivalence relation and the relation E1 of eventual equality of sequences of reals. Thus quasi-isometry of finitely generated groups is not Borel reducible to the orbit relation of any Borel action of a Polish group. In particular, it is not essentially countable, answering a further question of Thomas. The constructions use doubles of a fixed finitely generated group over infinitely generated subgroups. Geodesic patterns recover the subgroups up to commensurability after conjugation in a fixed pattern-symmetry group, while an explicit gluing argument makes balanced finite-index changes invisible to quasi-isometry.

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• 10.5281/zenodo.234200872026

  Bi-orderable soluble groups with only Conradian left orders

  Martino Lupini · Orderability, Groups

  We prove that a soluble bi-orderable group all of whose left orders are Conradian is locally nilpotent, without any finite-generation or countability assumption. Consequently, every subgroup of such a group also has only Conradian left orders. This answers the soluble, bi-orderable case of the subgroup question posed by A. H. Rhemtulla and recorded in 2009.

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• 10.5281/zenodo.234199962026

  Thompson's group F′ is an O*-group: Positive conjugacy semigroups in Thompson's group F′

  Martino Lupini · Thompson groups, Orderability, Groups

  We give an explicit countable simple example for the Mal’cev–Fuchs question whether a simple O*-group exists, posed in 1963 and 1965. Every bi-invariant partial order on the commutator subgroup F′ of Thompson’s group F extends to a bi-invariant total order. Every partial positive cone lies in one of four cones determined by slopes at the leftmost or rightmost support endpoint. The central ingredient is a factorization theorem for right-moving one-bump maps with the same support: equality of their two endpoint slopes is equivalent to a sufficiently large power of one being a product of the corresponding number of conjugates of the other, supported on that interval. The proof combines bounded drift in orbit coordinates with a uniform correction bound from the commutator width of F′.

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• 10.5281/zenodo.234196352026

  Saturation and equational hulls of ordered semigroup varieties

  Martino Lupini · Orderability

  We prove that an inequality-defined variety of partially ordered semigroups is saturated if and only if the ordinary semigroup variety generated by its reducts is saturated. Here saturation excludes proper epimorphic extensions in the ambient category of all semigroups or all partially ordered semigroups. This transfers ordinary equational saturation criteria to compatible partial orders without finiteness, permutation, or convexity assumptions. It recovers a positive answer to Ahanger, Shah, and Khan’s question about ordered normal bands and gives a general equational framework for relaxing convexity in related saturation results. The proof uses the completely regular core E(S)SE(S), a bounded-exponent variety symmetry theorem, and a countable construction for arbitrary inequational theories.

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• 10.5281/zenodo.234195772026

  Amalgamation in an infinite chain of commutative idempotent residuated-lattice varieties

  Martino Lupini · Mathematics

  We construct a strictly increasing infinite chain of finitely generated varieties of commutative idempotent residuated lattices, each with the amalgamation property. The generator of Vₙ is a quasiprimal (n+3)-element algebra obtained by adjoining an absorbing least element to a bounded lattice with n incomparable interior elements; multiplication is join elsewhere. Homogeneity, congruence extension, and the classical homomorphism-extension method yield amalgamation. For n ≥ 2 the varieties are not semilinear, and for n ≥ 3 they are not lattice-distributive. This answers negatively the unrestricted finiteness question posed by Fussner, Metcalfe, and Santschi in Interpolation and the Exchange Rule, circulated in 2023 and published in 2026. The distributive version remains open. Among finite Stanovský algebras L⁰, amalgamation holds exactly when the interior of L is an antichain. Strong amalgamation holds for V₀ and fails for every Vₙ with n ≥ 1.

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• 10.5281/zenodo.234193932026

  The variety of integral residuated lattices fails the amalgamation property

  Martino Lupini · Mathematics

  We answer negatively the open question whether integral residuated lattices have the amalgamation property, recorded by Metcalfe, Paoli, and Tsinakis in their 2023 monograph and explicitly posed by Jipsen and Santschi in Residuated lattices do not have the amalgamation property. A span of finite integral residuated lattices, with a three-element common algebra and extensions of sizes five and six, has no amalgam even among all residuated lattices. Thus the three-element Gödel chain, in the signature without a bottom constant, is not an amalgamation base. The same example excludes amalgamation in every variety containing the five-element chain, including the varieties of n-potent integral residuated lattices for all n ≥ 2. We also isolate a local obstruction without global integrality assumptions and characterize amalgamation of a common-bottom quotient-product span by extension of the corresponding congruence.

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• 10.5281/zenodo.234182732026

  Isomorphism and bi-embeddability of countable Archimedean ordered groups

  Martino Lupini · Orderability, Descriptive set theory, Groups

  Let E and F denote order-preserving isomorphism and mutual order-preserving embeddability of countable Archimedean ordered groups. We prove that E

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• 10.5281/zenodo.234114932026

  Polarities, voltages, and capacitors: a categorical approach to hulls, envelopes, and completions

  Ivan Di Liberti, Martino Lupini · Orderability, C*-algebras

  This article provides a general framework in the context of category theory where one can recognize as particular instances of the same abstract construction several notions of completion, envelope, and hull, such as the completion of a Boolean algebra, the Dedekind–MacNeille completion of an ordered set, the multiplier ring of a ring, and the multiplier algebra of a C*-algebra.

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• 10.5281/zenodo.234077612026

  Lipschitz embeddings of symmetric operator-ideal balls into Hilbert space

  Martino Lupini · Operator algebras

  No abstract on this deposit.

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• 10.5281/zenodo.234055112026

  Bounded coordinate lengths and normal closures in Polish products

  Martino Lupini · Descriptive set theory, Groups

  We characterize when the abstract normal closure of an element of a countable product of arbitrary Polish groups admits a Polish group topology with the inherited Borel sets. For h=(hᵢ) in ∏ᵢLᵢ, put Bᵢ=hᵢ^{Lᵢ}(hᵢ⁻¹)^{Lᵢ} and Pᵢ=⟨Bᵢ⟩. The normal closure is Polishable precisely when every Pᵢ is Polishable and, for some integer k, Pᵢ=Bᵢᵏ outside finitely many coordinates. In this case it is the countable cyclic extension (∏ᵢPᵢ)⟨h⟩. Failure of the uniform bound yields a continuous injective reduction of E₁, eventual equality of sequences in 2^ℕ, to the coset relations of both the balanced and ordinary normal closures. The argument applies more generally to symmetric analytic coordinate generating sets. We also give an exact criterion for subgroups defined by uniformly bounded finite Borel coordinate lengths; their Polishable branch has coset relation either trivial or Borel bireducible with E₀. Applications include arbitrary nonabelian abstractly simple Polish factors and compact connected Lie factors. For projective unitary factors, a uniform spectral condition is equivalent to Polishability. Examples distinguish the coordinate obstruction, the uniform-width obstruction, and the cyclic obstruction to closedness.

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• 10.5281/zenodo.234055082026

  A universal Banach–Mazur stability radius for von Neumann algebras

  Martino Lupini · Mathematics

  We prove cohomological criteria for ordinary complex Banach–Mazur stability of von Neumann algebras, without separability, type, or density restrictions. A fixed algebra has a positive stability radius if its second bounded Hochschild cohomology vanishes and its third coboundary space is norm closed. For any class closed under countable bounded direct products, vanishing in degrees two and three gives one radius for the entire class. Assuming the degree-two and degree-three vanishing theorem in the September 2026 preprint of OpenAI, this yields one $\varepsilon>0$ such that, for all complex von Neumann algebras $M,N$,

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• 10.5281/zenodo.234048042026

  Polynomial estimates for K-convexity from Walsh decay and cotype

  Martino Lupini · Mathematics

  We obtain polynomial bounds for the norm K(X) of the Rademacher projection on a Banach space X. If the probability-normalized Walsh transform on the s-dimensional cube has norm at most 1/2 on L2(X), then K(X) ≤ 9000s log(6000s2). Consequently, for each 1 < p ≤ 2, the type constant Tp(X) satisfies K(X) ≲p Tp(X)p/(p−1)(1 + log Tp(X)). This improves the exponential upper bound in Naor’s 2022 quantitative question, without determining optimal dependence.

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• 10.5281/zenodo.234046012026

  Recursive classification and admissible descent for preliminary C*-algebras with prescribed weighted spectrum

  Martino Lupini · C*-algebras

  We prove that compatible local separable preliminary C*-algebras on an open cover occur as the specified ideals of a global algebra exactly when their transported corona ranges are pairwise orthogonal. Here preliminary means that all irreducible representations are finite-dimensional. We fix a primitive spectrum X and positive integer representation dimensions w, with X second countable, locally compact, and sober and w satisfying the dimension-compatibility condition for preliminary spaces; realization of (X,w) is not assumed. The canonical homogeneous filtration is countable. Classical homogeneous classification and Busby extension theory then give an exact recursive classification by matrix bundles and attaching maps subject to a localized-kernel test for the prescribed topology. We organize these extension data by Čech cocycles satisfying corona orthogonality, modulo gauge and refinement, without reducing them to characteristic classes. A doubled-endpoint example exhibits a nonrealizable class in unrestricted nonabelian H¹. For constant weight n, admissibility is automatic and the invariant is the marked classical Fell–Tomiyama–Takesaki invariant Čech H¹(X,PU(n)). Geometric boundary models for two-stratum algebras allow singular multiplier fibres; explicit families yield attachment multiplicities and Fell ranks.

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• 10.5281/zenodo.234044292026

  Spectral ranks and dynamical lengths of preliminary C*-algebras

  Martino Lupini · C*-algebras, Descriptive set theory

  We classify the spectral ranks and automorphism lengths of nonzero separable preliminary C*-algebras, whose irreducible representations are all finite-dimensional. The spectral invariants are the Fell rank ρ and the Pedersen rank β of the irreducible-dimension function. Automorphism length q measures the transfinite descriptive complexity of automorphisms modulo those implemented by multiplier unitaries; its fractional values distinguish terminal Borel classes.

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• 10.5281/zenodo.233963312026

  Support rings, Polishability, and the SIN property

  Martino Lupini · Descriptive set theory, Groups

  Let T be a finite nontrivial group and I countable. We prove that a Borel subgroup P ≤ TI is Polishable whenever its realized supports form a Polishable Boolean ring ℬ and each principal-support group PA, A ∈ ℬ, has an exact coordinate frame over T[ℬ|A]. This includes groups locally contained in finite direct powers of a finite quasisimple group. In that case, P admits a compatible Polish SIN topology exactly when its support ring admits a compatible Polish additive topology with a downward-closed neighborhood base. Solid support topologies also give a global frame and a complete bi-invariant metric. For abstract groups locally contained in finite powers of a finite nonabelian simple group S, the same SIN criterion uses the Boolean ring of principal normal subgroups; its locally compact instances are SJ × D, with J at most countable and D countable discrete. We further prove that principally trivial Boolean-ring covers preserve Polishability for every finite deck group. The proofs use frame-independent category and Polish group extensions. Explicit counterexamples delimit the coefficient, coordinate-projection, intrinsic and finite-deck hypotheses.

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• 10.5281/zenodo.233835602026

  Proximally irreducible affine extensions: composition and maximal covers

  Martino Lupini · Groups

  We prove that the composition of proximally irreducible affine extensions is proximally irreducible, answering a question of Bal for arbitrary topological groups and compact Hausdorff affine flows. The proof combines localization, Baire category, and compactness for finite convex witnesses, without requiring closed extreme-point sets. Composition, factorization, inverse limits, and uniform density bounds yield maximal proximally irreducible covers, unique up to a unique isomorphism over the base and characterized by a universal property. Extensions of a fixed base form a complete lattice, realized by closed invariant spaces of affine functions on its maximal cover. Passing to probability flows recovers maximal proximal covers of minimal flows and gives canonical refinements, pullbacks, and functorial lifts. For the trivial group, Gleason covers describe maximal domains and classify polytope extension lattices. For separable groups, extensions of metrizable bases admit metrizable approximations that detect nontriviality. Examples delimit the affine pullback and metrizability statements.

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• 10.5281/zenodo.233732062026

  A counterexample to the Global Glimm Problem

  Martino Lupini · C*-algebras

  We construct a unital, separable, nuclear C*-algebra whose hereditary subalgebras have no nonzero finite-dimensional representations, but which has no full square-zero element. This gives negative answers to the Global Glimm Problem, originating in Kirchberg and Rørdam’s work, and to Elliott and Rørdam’s full matrix-cone question. The algebra is a continuous field of CAR algebras over a countable product of finite quaternionic projective spaces. Every selfadjoint element is scalar in some fiber; consequently, there are no two orthogonal full positive elements and no full soft positive element. The construction realizes Dranishnikov–Levin’s equivariant obstruction in quaternionic bundles within the CAR-field framework of Hirshberg, Rørdam, and Winter.

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• 10.5281/zenodo.233720662026

  Finite sums and idempotency for dynamically central piecewise syndetic sets

  Martino Lupini · Mathematics

  A set of positive integers is a set of pointwise recurrence if it supplies a return of every point to every neighborhood of itself in every minimal topological dynamical system. We prove that every such set contains finite-sums configurations of every finite rank. More generally, this holds after intersection with a return set to a neighborhood of a point in a minimal system: every dynamically central piecewise syndetic set is IP₀. The finite-sums configurations can be chosen with a piecewise syndetic set of simultaneous completions; their generators may be taken superincreasing.

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• 10.5281/zenodo.233716902026

  Pointwise convergence of bilinear averages for two commuting transformations

  Martino Lupini · Mathematics

  Let T and S be commuting measure-preserving transformations of a probability space. We prove that, for f,g ∈ L³, the bilinear averages (1/N)∑ₙ₌₁ᴺ f(Tⁿx)g(Sⁿx) converge almost everywhere and satisfy an L³ᐟ² bound for their full r-variation for every r > 2. In particular, this answers the bounded-input convergence question recorded as Problem 19 in Frantzikinakis’s 2016 survey, without an invertibility assumption.

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• 10.5281/zenodo.233625992026

  Exactness and amenability at infinity for locally compact groupoids

  Martino Lupini · Groupoids, Amenability, Groups

  For a second-countable locally compact Hausdorff étale groupoid G, we prove the equivalence of exactness of Cr*(G), exactness of reduced crossed products, and strong amenability at infinity. These conditions are also equivalent to exactness of any one twisted reduced algebra. The amenable action can be chosen with a proper open surjective anchor admitting a continuous section. This answers Anantharaman–Delaroche’s 2016 exactness questions and the étale case of LaLonde’s 2017 question about exact transformation groupoids. Consequently, exactness together with canonical weak containment implies amenability; for compact unit space, exactness is equivalent to amenability of the Furstenberg boundary action. We also prove permanence of strong amenability at infinity under continuous strongly surjective homomorphisms between second-countable groupoids with Haar systems, when the kernel and target have this property. No Haar system on the kernel is required. Finally, we construct an inner-exact étale group bundle with exact fibers and nonexact reduced algebra, supplying the example asked for by Anantharaman–Delaroche in 2016 and answering LaLonde’s 2017 group-bundle question negatively. Its fibers are hyperbolic groups converging strongly to a free group, while their Cayley graphs fail uniform property A.

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• 10.5281/zenodo.233485852026

  Dynamical spectra of unital C*-algebras: AF realizations and Cartan pairs

  Martino Lupini · C*-algebras, Groupoids, Descriptive set theory

  For a separable unital C*-algebra, the dynamical length records the descriptive complexity of its inner derivations and inner automorphisms. For a Cartan pair, it also records two cohomological lengths of the Weyl groupoid and the length of the automorphism group preserving the Cartan subalgebra. We determine the spectra of AF algebras, standard AF pairs, C*-diagonals in AF algebras, and arbitrary Cartan pairs whose ambient algebra is AF. Nonconstant tuples form a finite list at the bottom of the scale. The positive constant coordinates are exactly {β+1 : β<ω₁} ∪ {α+1/2, α+1/2+ε : 0<α<ω₁}, where the half-step symbols are formal indices in the scale. We construct the fractional realizations through zero-dimensional incidence systems and prove that every positive derivation length of a separable unital C*-algebra has a standard AF-pair realization. Each positive value has a standard diagonal realization in a separable unital 2-subhomogeneous AF algebra satisfying Fell's condition. The absolute spectrum of all separable unital C*-algebras coincides with the AF spectrum, and the spectrum of Kumjian diagonal pairs coincides with that of standard AF pairs. General Cartan pairs have one additional low value. We also determine the spectra within the scattered, continuous-trace, simple, and homogeneous classes. The exclusion of the remaining fractional candidates is imported from a companion theorem.

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• 10.5281/zenodo.233440132026

  Injective and projective objects in categories of topological torsion Polish abelian groups

  Martino Lupini · Descriptive set theory, Groups

  We give complete proofs of the injective and projective classifications in four categories of non-Archimedean Polish abelian groups, according to whether the groups are locally compact and whether their discrete quotients are torsion or p-primary. The new results characterize projectives without a local compactness assumption: they are precisely the compact torsion-free groups, namely products over primes p of powers of Z_p in the torsion case and powers of Z_p in the p-primary case, with all multiplicities at most countable. These results answer two questions posed by Casarosa, Codenotti, and Lupini in 2024. We also prove their known injective classifications: the locally compact injectives are the countable discrete divisible groups of the relevant prime class, and the injectives in the larger categories are countable products of such groups. None of the four categories has enough projectives, and precisely the compact objects admit strict projective resolutions. The two larger categories have enough injectives; in the locally compact categories, precisely the discrete objects embed strictly into injectives. We also characterize injectives and projectives in all four left hearts: only zero is injective, and the projectives remain exactly the compact torsion-free groups. The locally compact left-heart results are known; for the two larger hearts, the absence of nonzero injectives follows from an argument using Solecki ranks.

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• 10.5281/zenodo.233423112026

  Dynamical length of Cartan pairs: comparison, rigidity, and invariance

  Martino Lupini · Orderability, C*-algebras, Groupoids

  A Cartan subalgebra permits a separable unital C*-algebra to be studied through its twisted étale Weyl groupoid. We combine five cohomological, derivation, and automorphism lengths into the dynamical length ℓ(A,D) of a Cartan pair. These lengths measure the accumulation of coboundaries and inner symmetries through the canonical filtration of phantom subgroups.

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• 10.5281/zenodo.233421992026

  Efficient contractions of the Urysohn isometry group

  Martino Lupini · Descriptive set theory, Groups

  We construct a contraction of the Urysohn isometry group with uniform and coarse control. Pointwise stabilizers of nonempty finite sets admit contractions uniformly continuous for the left uniformity, and the global contraction preserves bounded-displacement sets. Ordinary contractibility is due to Melleray, while the quantitative realization and embedding inputs are due to Lešnik. The construction here adds guided surjective back-and-forth, inverse evaluation control, and uniform endpoint estimates. A preliminary bounded-chain argument shows that the bounded-image clause of efficient contractibility follows from the stated uniform-continuity hypothesis.

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• 10.5281/zenodo.233421812026

  Bounded geometry in Polish groups: locally compact models, amenability, and simple examples

  Martino Lupini · Orderability, Descriptive set theory, Amenability

  We develop locally compact models and applications for Polish groups of bounded geometry. Building on Hrushovski's quasi-model theorem and the ultrafilter framework of Krupiński–Pillay, we give an explicit coarse-density calculation for a model with compact conjugation-invariant multiplication defect and exact control of the intrinsic coarsely bounded bornology. Applications yield the Haagerup property under topological amenability and two-sided entropy estimates under metric amenability. Packing and model obstructions treat the stated classes of groups. For McCleary's classical simple periodic coloured-order group, we compute the pointwise Polish topology and intrinsic coarse geometry, obtaining a non-locally compact quasi-line.

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• 10.5281/zenodo.233421522026

  Pointwise bounded cocycles and coarse decompositions of topological groups

  Martino Lupini · Descriptive set theory, Groups

  We prove a uniform-boundedness principle for Borel cocycles between Polish groups: pointwise coarsely bounded fibres are uniformly coarsely bounded over each coarsely bounded subset of the acting group. A bounded-defect version applies to quasicocycles. The principle yields a Zappa–Szép coarse-product criterion without local boundedness and a nonsplit-extension criterion using Borel sections and pointwise intrinsic bounds, without a centralizing-section hypothesis. We also prove that local boundedness lifts through ultralocally bounded quotients. Supplementary sections give conditional coupling-composition results and examine category assumptions in factorization, using a classical additive-graph construction.

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• 10.5281/zenodo.233421262026

  Boundedness exponents of unitary function groups and measured full groups

  Martino Lupini · Descriptive set theory, Groups

  Let $X$ be an infinite compact metrizable space and let $M\ne0$ be a von Neumann algebra with separable predual. For the strong topology on $\mathcal{U}(M)$, we classify boundedness of $C(X,\mathcal{U}(M))$: finite exponents occur exactly when $M$ is properly infinite, with least open-exhaustion exponent five and least finite-neighbourhood exponent three, and ordinary Property $(\mathrm{OB})$ holds exactly when $\dim X=0$ or $M$ has no matrix direct summand. Continuous fixed-involution factors give the finite-exponent result; compact-uniform adaptations of spectral regularization and central splitting give ordinary boundedness. The classification concerns function-group boundedness, while the corresponding target contractibility criterion is due to Jekel. Related four-factor target-unitary and type III full-group bounds are upper bounds.

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• 10.5281/zenodo.233421102026

  Exact boundedness exponents for permutation and automorphism groups

  Martino Lupini · Descriptive set theory, Groups

  We determine exact boundedness exponents for automorphism groups in the pointwise topology. For countably infinite-dimensional vector spaces over countable fields, general linear groups have least open-exhaustion exponent three over finite fields and four over infinite fields. Symplectic groups for the standard alternating form have corresponding exponents three and five. Orthogonal groups for the form $B(x,y)=\sum_i x_i y_i$ have the same three-versus-five dichotomy in characteristic different from two. The automorphism group of a free abelian group of countably infinite rank has least open-exhaustion exponent five. Routing and reflection give exact exponent-four results for unrestricted permutation wreath products. A directional fresh-copy criterion and function-group applications supplement these calculations.

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• 10.5281/zenodo.233420552026

  Quantitative boundedness in homeomorphism groups

  Martino Lupini · Descriptive set theory, Groups

  We obtain sharp boundedness exponents from finite-correction obstructions and continuously varying geometric normal forms. With the compact-open topology, the homeomorphism group of the two-sphere and the full and orientation-preserving homeomorphism groups of planar telescoping surfaces have least open-exhaustion exponent five and least finite-neighbourhood exponent three. The same pair holds for continuous-function groups from nonempty nondiscrete locally compact second-countable Hausdorff spaces into the boundary-fixing homeomorphism group of a ball of any positive dimension. Five-factor bounds for further geometric targets refine known qualitative boundedness arguments; the full-sphere bound and the pointwise boundary-fixing ball word already occur in published proofs. A controlled Hilbert-cube argument supplies a quantitative bound and repairs the earlier qualitative proof. We also extend ultralocal boundedness from closed compact manifolds to compact manifolds with boundary.

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• 10.5281/zenodo.233420182026

  Fixed words, function groups, and exact odd boundedness exponents

  Martino Lupini · Descriptive set theory, Groups

  For an infinite zero-dimensional compact metrizable space $X$ and a Polish group $P$, we characterize boundedness with a fixed number of factors of $C(X,P)$ by words alternating a target identity neighbourhood with fixed elements. If the least number of neighbourhood factors required for every identity neighbourhood of $P$ is $k$, then $C(X,P)$ has least finite-neighbourhood exponent $k$ and least open-exhaustion exponent $2k-1$. Neither exponent is finite when no such $k$ exists. Matching word bounds for circular covering groups then realize every odd least open-exhaustion exponent at least five, both among non-Archimedean Polish groups and among path-connected locally contractible Polish groups. We also establish an ordinary-boundedness criterion and transfer results for continuous and measurable function groups.

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• 10.5281/zenodo.233419432026

  Fixed-exponent boundedness and cocompact permanence in Polish groups

  Martino Lupini · Descriptive set theory, Groups

  We prove that closed cocompact inclusions and compact normal quotients preserve each fixed open-exhaustion and finite-neighbourhood exponent for Polish groups. The literal open-exhaustion conditions and the finite-neighbourhood conditions have distinct indices, related by an explicit interlacing calculus. We also obtain extension and product bounds. We also give a corrected proof of the previously stated coarse equivalence between a Polish group and a closed cocompact subgroup, using compact transition sets. The final section collects consequences and examples for groups whose coarsely bounded sets are relatively compact.

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• 10.5281/zenodo.233411642026

  Solution to Dixmier's Problem about spectra of C*-algebras

  Martino Lupini · Orderability, C*-algebras, Descriptive set theory

  Dixmier asked in 1967 whether the spectra of simple separable non-type-I C*-algebras all have the same Borel structure. We solve the formulation using ordinary isomorphisms of quotient Borel σ-algebras by proving that its universal assertion is independent of ZFC, relative to the consistency of ZFC. Under the continuum hypothesis, all separable non-type-I spectra are measurably isomorphic, without simplicity or unitality assumptions. In the model obtained by iterating Sacks forcing for ω₂ stages with countable supports over a GCH ground model, a fixed simple unital universal spectrum is not measurably isomorphic to the CAR spectrum. Neither consistency direction requires a large cardinal.

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• 10.5281/zenodo.233387882026

  Automatic equivariant Jiang–Su stability in the nonunital tracial setting

  Martino Lupini · C*-algebras, Amenability, Groups

  Let A be a separable simple nuclear C*-algebra that absorbs the Jiang–Su algebra Z and admits a nonzero densely defined lower semicontinuous trace. Using the Gaussian construction of the October 2026 OpenAI preprint, we prove that every action α of a countable discrete amenable group on A is cocycle conjugate to α ⊗ idZ. This answers the general tracial part of Szabó’s 2019 conjecture on automatic equivariant Jiang–Su stability, extending the October 2026 unital theorem to algebras with possibly unbounded traces and to trace-scaling actions. The extension applies that construction in a tracial quotient of Kirchberg’s central sequence algebra and uses the nonunital absorption results of Szabó and Wouters. The transfer is expressed as a local equivariant Gamma criterion for nonseparable unital algebras admitting relative copies of Z. Its uniform trace-splitting estimates allow the original action and its full cone of traces to be retained. Combined with the established purely infinite case, the result gives automatic equivariant Jiang–Su stability for all separable simple nuclear Z-stable algebras.

  PDF · LaTeX · GitHub named

• 10.5281/zenodo.232914592026

  Sharp Borel representation dimensions for compact arithmetic actions

  Martino Lupini · Descriptive set theory

  No abstract on this deposit.

  PDF · LaTeX · Python · Data

• 10.5281/zenodo.232914432026

  Arithmetic denominators and ordinary compact orbit comparisons

  Martino Lupini · Mathematics

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.232914082026

  Measurable signatures and algebraic structure of L¹ full groups

  Martino Lupini · Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.232914012026

  Local swaps, Polish group topologies, and automorphisms of L¹ full groups

  Martino Lupini · Descriptive set theory, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.232913922026

  Polish topologies and coset obstructions for measurable transformation groups

  Martino Lupini · Descriptive set theory, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.232847082026

  A three-generated abelian lattice-ordered group without an existentially closed prime extension

  Martino Lupini · Orderability, Groups

  No abstract on this deposit.

  PDF

• 10.5281/zenodo.232775982026

  Distributivity of lattice-ordered pregroups

  Martino Lupini · Orderability

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.232767792026

  Local fields and ordinary affine Borel comparisons

  Martino Lupini · Descriptive set theory

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.231768272026

  Convex normal subgroups of ℓ-simple lattice-ordered groups

  Martino Lupini · Orderability, Groups

  We construct a countable nonabelian normal-valued lattice-ordered group G which is ℓ-simple and has a nontrivial proper ordinary convex normal subgroup N. Both N and its abelian lattice hull H are free abelian of countably infinite rank. The subgroup N is an antichain normally generated by one element, while H is proper, normal, cofinal and order dense. This answers Problem 1.1 of Bludov, Glass, Kopytov and Medvedev negatively. Finite triangular coefficient tables on lexicographically ordered blocks preserve the antichain. A positive element forces an ordinary convex normal subgroup to contain the entire next finite-table group; iteration therefore gives simplicity. A conjugating extension and order density show that every positive nonidentity element of G has a cofinal conjugacy class. For an ℓ-simple group, a strong order unit guarantees an affirmative answer. We derive strong order units from finite lattice generation, a finite-index commensurator of a nontrivial finitely generated subgroup, or a nontrivial normal subgroup whose elements have powers in a fixed finitely generated subgroup.

  PDF · LaTeX · Data

• 10.5281/zenodo.231718172026

  Tame functions and Asplund representations of additive Banach groups

  Martino Lupini · Operator algebras, Groups

  We prove that tame functions on the additive group of c0 do not determine its norm topology, answering questions of Megrelishvili and Glasner–Megrelishvili. The proof combines Gowers’ positive-block stabilization with Megrelishvili’s independent-translates configuration. The obstruction extends by homomorphism pullback to Banach spaces containing c0. Full-sphere stabilization gives arbitrarily large subspace balls of approximate constancy and shows that every point of a closed norm ball lies in the tame closure of its boundary sphere. In contrast, a dyadic phase map and the coordinate-rotation construction of Antunes, Ferenczi, Grivaux and Rosendal give a strong-operator embedding of c0 into the isometry group of an Asplund space isomorphic to c0, with almost periodic scalar coefficients. Thus c0 is Asplund but not reflexively representable, settling the Asplund-versus-reflexive problem; even its tame algebra fails to determine the topology. Applications give local copies of βℕ in every proper semigroup compactification and exclude c0 from compact-open automorphism groups of finite-rank compact topological median algebras. For locally compact abelian H, tame functions determine the uniform topology of c0(H) exactly when H is totally disconnected. For second-countable H, these groups are always Asplund representable.

  PDF · LaTeX · Data

• 10.5281/zenodo.231695762026

  Polishability from orbit reducibility of coset equivalence relations

  Martino Lupini · Descriptive set theory, Groups

  We prove that a Borel subgroup H of a Polish group G is Polishable if and only if its coset equivalence relation is Borel reducible to the orbit equivalence relation of a Borel action of a Polish group. The proof combines Jankov–von Neumann uniformization with an invariant category criterion derived from Solecki's approximation theorems. Averaging the canonical category ideals of the target orbits over G supplies the invariant ideal needed for recognition. Consequently, a non-Polishable Borel subgroup has a coset relation that is not classifiable by countable structures.

  PDF · LaTeX

• 10.5281/zenodo.231424712026

  The linear isometry group of the Holmes space

  Martino Lupini · Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.231332632026

  Universal minimal flows of automorphism groups of locally finite trees

  Martino Lupini · Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.231257522026

  The Artin group of type $E_8$ and the left-orderability of spherical Artin groups

  Martino Lupini · Orderability, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.231141372026

  Injective objects in the category of Polish abelian groups

  Alessandro Codenotti, Martino Lupini · Descriptive set theory, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.231060642026

  Constructive normal identities in metabelian groups

  Martino Lupini · Groups

  No abstract on this deposit.

  PDF · LaTeX · Data

• 10.5281/zenodo.231050332026

  An eight-element parachute lattice and its dual: finite representations with two unary operations

  Martino Lupini · Mathematics

  No abstract on this deposit.

  PDF · LaTeX · Notes · Data

• 10.5281/zenodo.230466982026

  A countable lattice-ordered group not latticeisomorphic to any abelian one

  Martino Lupini · Orderability, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.230461692026

  Property (OB) and the Coarse Geometry of Polish Groups --- Fixed Exponents, Permanence, and Applications

  Martino Lupini · Descriptive set theory, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.229325952026

  Lattice-Ordered Groups as Full Automorphism Groups of Posets

  Martino Lupini · Orderability, Posets, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.229324302026

  A subdirect product of Ohkuma groups with nonunique addition

  Martino Lupini · Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.229298252026

  Continuous Lipschitz spaces on topometric spaces and free-space dynamics

  Martino Lupini · Mathematics

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.229297642026

  The countable cube with the supremum metric is not Lipschitz universal

  Martino Lupini · Mathematics

  The countable cube with the supremum metric is not Lipschitz universal

  PDF · LaTeX

• 10.5281/zenodo.229237112026

  Norm formulas, independence, and spaces of types

  Martino Lupini · Mathematics

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228906182026

  Rosenthal representations of homogeneous spaces: rank-one classifications and higher-rank criteria

  Martino Lupini · Mathematics

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228863602026

  Low-complexity factors of compact affine semigroup actions

  Martino Lupini · Mathematics

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228862952026

  Convergence relations of pro-Lie Polish groups

  Martino Lupini · Descriptive set theory, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228833532026

  Isomorphism of finitely generated bi-orderable elementary amenable groups is universal

  Martino Lupini · Orderability, Amenability, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228829562026

  Rank-two and two-prime rigidity in Borel classification problems

  Martino Lupini · Descriptive set theory

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228526312026

  Ordered Compactifications and Circular Ellis Semigroups

  Martino Lupini · Orderability

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228473142026

  Uniform cohomological gaps and operator-local repair

  Martino Lupini · Operator algebras

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228452362026

  Skew-amenability in finite-regularity topologies for path, loop, and gauge groups

  Martino Lupini · Amenability, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228433542026

  Nonabelian extensions of Solecki's coset dichotomy

  Martino Lupini · Mathematics

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228428972026

  Twisted Iwahori gluing and central extensions of SL2(Z[1/2])

  Martino Lupini · Mathematics

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228399152026

  Charmenability of Leavitt unit groups and Clifford-lamp groups

  Martino Lupini · Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228398652026

  UCT-universal nuclear quotients of a binary wreath product

  Martino Lupini · Mathematics

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228341372026

  Congruence stability for an Iwahori gluing problem

  Martino Lupini · Mathematics

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228340732026

  Contractibility and Banach-space representations of the Carderi--Thom groups

  Martino Lupini · Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228294622026

  LoCoLoCo Polish subgroups and the non-Archimedean complexity spectrum

  Martino Lupini · Descriptive set theory

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228167792026

  Joint Euler-cocycle estimates and simplicial volume of surface bundles

  Martino Lupini · Mathematics

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228146892026

  $\mathbf{\Sigma^0_2}$ boundaries in $\ell^1$-homology from amenable convergence actions

  Martino Lupini · Amenability

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228137522026

  A matrix convexity characterization of the noncommutative Poulsen simplex

  Martino Lupini · Mathematics

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228133152026

  Malliavin--Malliavin and whirly amenability: Borel observations, translation displacement, and total variation

  Martino Lupini · Descriptive set theory, Amenability

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228131892026

  Distortion of Banach-space unit spheres under their linear isometry groups

  Martino Lupini · Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228097652026

  Generic monothetic subgroups of the measure automorphism group

  Martino Lupini · Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.227764742026

  Universal minimal flows of homeomorphism groups of solenoids and Knaster continua

  Martino Lupini · Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.227750142026

  Exactness of strong unitary groups associated with discrete groups with the approximation property

  Martino Lupini · Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.227646152026

  Universal minimal flows of automorphism groups\\of stable Kirchberg algebras

  Martino Lupini · Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.227616302026

  Universal minimal flows for unital Kirchberg and AF algebras

  Martino Lupini · Mathematics

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.227583052026

  Circular colorings of abelian Cayley graphs below four

  Martino Lupini · Mathematics

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.227582302026

  Borel invariant means on countable inverse limits of amenable groups

  Martino Lupini · Descriptive set theory, Amenability, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.227493622026

  Whirly monothetic groups that are not L\'evy

  Martino Lupini · Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.227436042026

  Amenability and skew-amenability of C1 path, loop, and one-dimensional gauge groups

  Martino Lupini · Amenability, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.227378542026

  Concentrating measures and whirly amenability of Doucha's universal metric group

  Martino Lupini · Amenability, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.227378282026

  L\'evy stabilizers of the Poulsen simplex, the Gurarij space, and their noncommutative analogues

  Martino Lupini · Mathematics

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.227375692026

  Universal minimal flows of inductive limits of Lie groups

  Alessandro Codenotti, Martino Lupini · Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.227374132026

  A counterexample to the (approximate) Universal Coefficient Theorem for \texorpdfstring{$K$}{K}-homology of C*-algebras

  Martino Lupini · C*-algebras

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.227224532026

  Extreme amenability of the automorphism group of the Jiang-Su algebra

  Martino Lupini · Amenability, Groups

  No abstract on this deposit.

  PDF · LaTeX · Data

• 10.5281/zenodo.227221902026

  Extreme amenability of the automorphism group of the Razak-Jacelon algebra

  Martino Lupini · Amenability, Groups

  No abstract on this deposit.

  LaTeX · Data

• 10.5281/zenodo.227189882026

  Universal minimal flows of Cuntz automorphism and unitary groups

  Martino Lupini · Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.227135582026

  Extreme amenability of the additive group of $L^p$ for $0<p<1$

  Martino Lupini · Amenability, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.227011632026

  Borel-definable homological algebra for locally compact Polish modules over rings of integers

  Martino Lupini · Descriptive set theory

  No abstract on this deposit.

  PDF · LaTeX · Data

• 10.5281/zenodo.227010812026

  Homological algebra of pro-Lie Polish modules over rings of integers

  Martino Lupini · Descriptive set theory

  No abstract on this deposit.

  PDF · LaTeX · Data

• 10.5281/zenodo.226953502026

  Descriptive classification of classes of C*-algebras and locally compact groups

  Martino Lupini · C*-algebras, Descriptive set theory, Groups

  No abstract on this deposit.

  PDF · LaTeX · Data

• 10.5281/zenodo.226918402026

  Homogeneity of complete M-faces of the noncommutative Poulsen simplex

  Martino Lupini · Mathematics

  No abstract on this deposit.

  PDF · LaTeX · Data

• 10.5281/zenodo.226898792026

  The franks of Moore groups

  Alessandro Codenotti, Martino Lupini, Francesco Milizia · Groups

  No abstract on this deposit.

  PDF · LaTeX · Data

• 10.5281/zenodo.226870572026

  Derived limits and the phantom spectrum of Fréchet-Schwartz spaces

  Martino Lupini · Mathematics

  No abstract on this deposit.

  PDF · LaTeX · Data

• 10.5281/zenodo.226861732026

  Corrigendum to "Complexity Classes of Polishable Subgroups"

  Martino Lupini · Descriptive set theory

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.226858692026

  Dynamical spectra of separable unital scattered $C^*$-algebras and Cartan pairs

  Martino Lupini · Mathematics

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.226843792026

  Cohomological lengths of groupoids

  Martino Lupini · Groupoids

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.226842522026

  Normalizer correction and relative derivation and automorphism lengths for Cartan C*-subalgebras

  Martino Lupini · C*-algebras

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.226838592026

  Derivation length and automorphism length of unital C*-algebras

  Martino Lupini · C*-algebras

  No abstract on this deposit.

  PDF · LaTeX · Data

• 10.5281/zenodo.226833362026

  On the Borel complexity of operator images

  Martino Lupini · Operator algebras, Descriptive set theory

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.226763992026

  On Niemiec's Universal Valued Groups

  Alessandro Codenotti, Martino Lupini · Groups

  No abstract on this deposit.

  PDF · LaTeX · Data

• 10.5281/zenodo.226386402026

  C*-algebras of all successor ordinal derivation and automorphism lengths

  Martino Lupini · C*-algebras

  No abstract on this deposit.

  PDF · LaTeX · Data

• 10.5281/zenodo.225586172026

  Derived limits and phantom filtrations for towers of locally compact Polish abelian groups

  Martino Lupini · Descriptive set theory, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.223388852026

  The Descriptive Complexity of Nonabelian $\boldsymbol{\lim^1}$

  Matteo Casarosa, Martino Lupini · Descriptive set theory

  No abstract on this deposit.

  PDF · LaTeX · Data

• 10.5281/zenodo.223344012026

  Bratteli graphs

  Martino Lupini · Mathematics

  No abstract on this deposit.

  PDF · LaTeX · Data