Subject / 46 records

Homological algebra and derived limits

Exact completions, derived limits, phantom filtrations, cohomology, and UCT questions.

Classification: Second Brain

46 records

• 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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.

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• 10.5281/zenodo.232914432026

  Arithmetic denominators and ordinary compact orbit comparisons

  Martino Lupini · Mathematics

  No abstract on this deposit.

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• 10.5281/zenodo.232914082026

  Measurable signatures and algebraic structure of L¹ full groups

  Martino Lupini · Groups

  No abstract on this deposit.

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• 10.5281/zenodo.232913922026

  Polish topologies and coset obstructions for measurable transformation groups

  Martino Lupini · Descriptive set theory, Groups

  No abstract on this deposit.

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• 10.5281/zenodo.232775982026

  Distributivity of lattice-ordered pregroups

  Martino Lupini · Orderability

  No abstract on this deposit.

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• 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.

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• 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.

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• 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.

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• 10.5281/zenodo.231060642026

  Constructive normal identities in metabelian groups

  Martino Lupini · Groups

  No abstract on this deposit.

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• 10.5281/zenodo.229324302026

  A subdirect product of Ohkuma groups with nonunique addition

  Martino Lupini · Groups

  No abstract on this deposit.

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• 10.5281/zenodo.228473142026

  Uniform cohomological gaps and operator-local repair

  Martino Lupini · Operator algebras

  No abstract on this deposit.

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• 10.5281/zenodo.228398652026

  UCT-universal nuclear quotients of a binary wreath product

  Martino Lupini · Mathematics

  No abstract on this deposit.

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• 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.

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• 10.5281/zenodo.227375692026

  Universal minimal flows of inductive limits of Lie groups

  Alessandro Codenotti, Martino Lupini · Groups

  No abstract on this deposit.

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• 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.

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• 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.

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• 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.

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• 10.5281/zenodo.226870572026

  Derived limits and the phantom spectrum of Fréchet-Schwartz spaces

  Martino Lupini · Mathematics

  No abstract on this deposit.

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• 10.5281/zenodo.226843792026

  Cohomological lengths of groupoids

  Martino Lupini · Groupoids

  No abstract on this deposit.

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• 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.

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• 10.5281/zenodo.223388852026

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

  Matteo Casarosa, Martino Lupini · Descriptive set theory

  No abstract on this deposit.

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