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Structure invariant properties of the hierarchically hyperbolic boundary J. Topol. Anal. (IF 0.8) Pub Date : 2024-03-25 Carolyn Abbott, Jason Behrstock, Jacob Russell
We prove several topological and dynamical properties of the boundary of a hierarchically hyperbolic group are independent of the specific hierarchically hyperbolic structure. This is accomplished by proving that the boundary is invariant under a “maximization” procedure introduced by the first two authors and Durham.
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Persistent homotopy groups of metric spaces J. Topol. Anal. (IF 0.8) Pub Date : 2024-03-22 Facundo Mémoli, Ling Zhou
In this paper, we study notions of persistent homotopy groups of compact metric spaces. We pay particular attention to the case of fundamental groups, for which we obtain a more precise description via a persistent version of the notion of discrete fundamental groups due to Berestovskii–Plaut and Barcelo et al. Under fairly mild assumptions on the spaces, we prove that the persistent fundamental group
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A simpler proof of Sternfeld’s Theorem J. Topol. Anal. (IF 0.8) Pub Date : 2024-03-11 S. Dzhenzher
In Sternfeld’s work on Kolmogorov’s Superposition Theorem appeared the combinatorial–geometric notion of a basic set and a certain kind of arrays. A subset X⊂ℝn is basic if any continuous function X→ℝ could be represented as the sum of compositions of continuous functions ℝ→ℝ and projections to the coordinate axes. The definition of a Sternfeld array is presented in this paper. Sternfeld’s Arrays Theorem
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Double Johnson filtrations for mapping class groups J. Topol. Anal. (IF 0.8) Pub Date : 2024-03-09 Kazuo Habiro, Anderson Vera
In this paper, we first develop a general theory of Johnson filtrations and Johnson homomorphisms for a group G acting on another group K equipped with a filtration indexed by a “good” ordered commutative monoid. Then, specializing it to the case where the monoid is the additive monoid ℕ2 of pairs on non-negative integers, we obtain a theory of double Johnson filtrations and homomorphisms. We apply
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A refinement of Morse–Novikov cohomology on manifolds with boundary and the cohomology of the space of solutions of kerΔ𝜃 J. Topol. Anal. (IF 0.8) Pub Date : 2024-03-07 Qusay S. A. Al-Zamil
In this paper, we consider the Morse–Novikov coboundary operator d𝜃:Ωk(M)→Ωk+1(M) where [𝜃]∈HdR1(M), and which is given by d𝜃ω=ω̣+𝜃∧ω, and for which the associated Morse–Novikov cohomology groups are denoted by H𝜃k(M). The ultimate objective of this paper is to uncover more geometric and topological insights about H𝜃k(M) when the boundary of M is nonvanishing. To begin, we employ a different
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Finite presentations for the balanced superelliptic mapping class groups J. Topol. Anal. (IF 0.8) Pub Date : 2024-03-06 Susumu Hirose, Genki Omori
The balanced superelliptic mapping class group is the normalizer of the transformation group of the balanced superelliptic covering space in the mapping class group of the total surface. We give finite presentations for the balanced superelliptic mapping class groups of closed surfaces, surfaces with one marked point, and surfaces with one boundary component. To give these presentations, we construct
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Filling systems on surfaces J. Topol. Anal. (IF 0.8) Pub Date : 2024-03-06 Shiv Parsad, Bidyut Sanki
Let Fg be a closed orientable surface of genus g. A set Ω={γ1,…,γs} of pairwise non-homotopic simple closed curves on Fg is called a filling system or simply be filling of Fg, if Fg∖Ω is a disjoint union of b topological discs for some b≥1. A filling system is called minimally intersecting, if the total number of intersection points of the curves is minimum, or equivalently b=1. The size of a filling
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Computing cohomology groups that classify bundles of strongly self-absorbing C∗-algebras J. Topol. Anal. (IF 0.8) Pub Date : 2024-03-06 Marius Dadarlat, James E. McClure, Ulrich Pennig
Locally trivial bundles of C∗-algebras with fiber D⊗𝒦 for a strongly self-absorbing C∗-algebra D over a finite CW-complex X form a group ED1(X) that is the first group of a cohomology theory ED∗(X). In this paper, we compute these groups by expressing them in terms of ordinary cohomology and connective K-theory. To compare the C∗-algebraic version of gl1(KU) with its classical counterpart we also
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Central limit theorem for euclidean minimal spanning acycles J. Topol. Anal. (IF 0.8) Pub Date : 2024-02-29 Primoz Skraba, D. Yogeshwaran
In this paper, we investigate asymptotics for the minimal spanning acycles (MSAs) of the (Alpha)-Delaunay complex on a stationary Poisson process on ℝd,d≥2. MSAs are topological (or higher-dimensional) generalizations of minimal spanning trees. We establish a central limit theorem (CLT) for total weight of the MSA on a Poisson Alpha-Delaunay complex. Our approach also allows us to establish CLTs for
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Bounding the Lagrangian Hofer metric via barcodes J. Topol. Anal. (IF 0.8) Pub Date : 2024-02-29 Patricia Dietzsch
In this paper, we provide an upper bound on the Lagrangian Hofer distance between equators in the cylinder in terms of the barcode of persistent Floer homology. The bound consists of a weighted sum of the lengths of the finite bars and the spectral distance.
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A solvable extended logarithm of the Johnson homomorphism J. Topol. Anal. (IF 0.8) Pub Date : 2024-02-22 Takefumi Nosaka
Concerning Johnson’s homomorphism from the Torelli group, there are previous works to define a logarithm of the homomorphism, and give some extension of the logarithm. This paper considers exponential solvable elements in the mapping class group of a surface, and defines the logarithms of such elements.
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Morse homology for perturbed Dirac-harmonic maps into flat tori J. Topol. Anal. (IF 0.8) Pub Date : 2024-02-21 Takeshi Isobe
In this paper, we consider Morse theory for perturbed Dirac-harmonic maps into flat tori. We show that Morse homology can be defined for some classes of perturbations, and that it is determined by a homotopy type of the perturbations. We also give an explicit computation of the homology. As an application, we give a lower bound on the number of perturbed Dirac-harmonic maps in a given component for
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Scattering theory and an index theorem on the radial part of SL(2, ℝ) J. Topol. Anal. (IF 0.8) Pub Date : 2024-02-17 H. Inoue, S. Richard
We present the spectral and scattering theory of the Casimir operator acting on radial functions in L2(SL(2,ℝ)). After a suitable decomposition, these investigations consist in studying a family of differential operators acting on the half-line. For these operators, explicit expressions can be found for the resolvent, for the spectral density, and for the Møller wave operators, in terms of the Gauss
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Asymptotically flat Fredholm bundles and assembly J. Topol. Anal. (IF 0.8) Pub Date : 2024-02-14 Benedikt Hunger
Almost flat finitely generated projective Hilbert C∗-module bundles were successfully used by Hanke and Schick to prove special cases of the Strong Novikov Conjecture. Dadarlat later showed that it is possible to calculate the index of a K-homology class η∈K∗(M) twisted with an almost flat bundle in terms of the image of η under Lafforgue’s assembly map and the almost representation associated with
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A crossed homomorphism for groups acting on the circle J. Topol. Anal. (IF 0.8) Pub Date : 2024-02-05 Shuhei Maruyama
In this paper, we construct a crossed homomorphism by using a group action on the circle and the Poincaré translation number. We relate it to the Euler class of the action in terms of the Hochschild–Serre spectral sequence. As an application, we answer a question of Calegari and Chen, which is on an explicit form of a certain crossed homomorphism on the mapping class group of the sphere minus a Cantor
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Analytic automorphism group and similar representation of analytic functions J. Topol. Anal. (IF 0.8) Pub Date : 2024-01-31 Bingzhe Hou, Chunlan Jiang
In geometry group theory, one of the milestones is Gromov’s polynomial growth theorem: Finitely generated groups have polynomial growth if and only if they are virtually nilpotent. Inspired by Gromov’s work, we introduce the growth types of weighted Hardy spaces. In this paper, we focus on the weighted Hardy spaces of polynomial growth, which cover the classical Hardy space, weighted Bergman spaces
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Resolution of singular fibers of an S1-manifold J. Topol. Anal. (IF 0.8) Pub Date : 2024-01-24 Yi-Sheng Wang
In this paper, we present a resolution of discrete singular fibers of a closed 5-manifold equipped with a locally free S1-action, and prove its compatibility with the resolution of cyclic surface singularities in the quotient orbifold by the S1-action.
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A finite presentation for the balanced superelliptic handlebody group J. Topol. Anal. (IF 0.8) Pub Date : 2024-01-03 Genki Omori, Yuya Yoshida
The balanced superelliptic handlebody group is the normalizer of the transformation group of the balanced superelliptic covering space in the handlebody group of the total space. We give a finite presentation for the balanced superelliptic handlebody group. To give this presentation, we construct a finite presentation for the liftable Hilden group.
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Wide short geodesic loops on closed Riemannian manifolds J. Topol. Anal. (IF 0.8) Pub Date : 2024-01-03 Regina Rotman
It is not known whether or not the length of the shortest periodic geodesic on a closed Riemannian manifold Mn can be majorized by c(n)vol1n, or c̃(n)d, where n is the dimension of Mn, vol denotes the volume of Mn, and d denotes its diameter. In this paper, we will prove that for each 𝜖>0 one can find such estimates for the length of a geodesic loop with angle between π−𝜖 and π with an explicit constant
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Morse functions and real Lagrangian thimbles on adjoint orbits J. Topol. Anal. (IF 0.8) Pub Date : 2023-12-28 Elizabeth Gasparim, Luiz A. B. San Martin
We compare Lagrangian thimbles for the potential of a Landau–Ginzburg model to the Morse theory of its real part. We explore Landau–Ginzburg models defined using Lie theory, constructing their real Lagrangian thimbles explicitly and comparing them to the stable and unstable manifolds of the real gradient flow.
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Unitary connections on Bratteli diagrams J. Topol. Anal. (IF 0.8) Pub Date : 2023-12-28 Paramita Das, Mainak Ghosh, Shamindra Ghosh, Corey Jones
In this paper, we extend Ocneanu’s theory of connections on graphs to define a 2-category whose 0-cells are tracial Bratteli diagrams, and whose 1-cells are generalizations of unitary connections. We show that this 2-category admits an embedding into the 2-category of hyperfinite von Neumann algebras, generalizing fundamental results from subfactor theory to a 2-categorical setting.
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Canonical nilpotent structure under bounded Ricci curvature and Reifenberg local covering geometry over regular limits J. Topol. Anal. (IF 0.8) Pub Date : 2023-12-28 Zuohai Jiang, Lingling Kong, Shicheng Xu
It is known that a closed collapsed Riemannian n-manifold (M,g) of bounded Ricci curvature and Reifenberg local covering geometry admits a nilpotent structure in the sense of Cheeger–Fukaya–Gromov with respect to a smoothed metric g(t). We study the nilpotent structures over a regular limit space with optimal regularities that describe the collapsing of original metric g, and prove that they are uniquely
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Energy estimates of Yang–Mills functional J. Topol. Anal. (IF 0.8) Pub Date : 2023-12-28 Teng Huang
In this paper, we use the Uhlenbeck compactness theorem and Lojasiewicz–Simon gradient inequality of the Yang–Mills L2-energy functional to prove some energy properties of Yang–Mills connections. In particular, we can get the discreteness of Yang–Mills energy from the compactness of the moduli space of Yang–Mills connections.
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Continuous dependence of curvature flow on initial conditions J. Topol. Anal. (IF 0.8) Pub Date : 2023-12-14 Michael Gene Dobbins
We study the evolution of a Jordan curve on the two-sphere by curvature flow, also known as curve shortening flow, and by level-set flow, which is a weak formulation of curvature flow. We show that the evolution of the curve depends continuously on the initial curve in Fréchet distance in the case where the curve bisects the sphere. This even holds in the limit as time goes to infinity. This builds
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Bumpy metrics theorem for geodesic nets J. Topol. Anal. (IF 0.8) Pub Date : 2023-12-14 Bruno Staffa
Stationary geodesic networks are the analogs of closed geodesics whose domain is a graph instead of a circle. We prove that for a Baire-generic Riemannian metric on a smooth manifold M, all connected embedded stationary geodesic nets are nondegenerate.
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Reducing spheres of genus-2 Heegaard splitting of S3 J. Topol. Anal. (IF 0.8) Pub Date : 2023-12-14 Sreekrishna Palaparthi, Swapnendu Panda
The Goeritz group of the standard genus-g Heegaard splitting of the three sphere, Gg, acts on the space of isotopy classes of reducing spheres for this Heegaard splitting. Scharlemann [Automorphisms of the 3-sphere that preserve a genus two Heegaard splitting, Bol. Soc. Mat. Mexicana10 (2004) 503–514] uses this action to prove that G2 is finitely generated. In this paper, we give an algorithm to construct
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Reducible normal generators for mapping class groups are abundant J. Topol. Anal. (IF 0.8) Pub Date : 2023-12-14 Hyungryul Baik, Dongryul M. Kim, Chenxi Wu
In this paper, we study the normal generation of the mapping class group. We first show that a mapping class is a normal generator if its restriction on the invariant subsurface normally generates the (pure) mapping class group of the subsurface. As an application, we provided a criterion for reducible mapping classes to normally generate the mapping class groups in terms of its asymptotic translation
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Equivariant formality of the isotropy action on (ℤ2 ⊕ ℤ2)-symmetric spaces J. Topol. Anal. (IF 0.8) Pub Date : 2023-12-14 Manuel Amann, Andreas Kollross
Compact symmetric spaces are probably one of the most prominent class of formal spaces, i.e. of spaces where the rational homotopy type is a formal consequence of the rational cohomology algebra. As a generalization, it is even known that their isotropy action is equivariantly formal. In this paper, we show that (ℤ2⊕ℤ2)-symmetric spaces are equivariantly formal and formal in the sense of Sullivan,
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Growth rate of Dehn twist lattice points in Teichmüller space J. Topol. Anal. (IF 0.8) Pub Date : 2023-12-14 Jiawei Han
Athreya et al. [Lattice point asymptotics and volume growth on Teichmüller space, Duke Math. J.161 (2012) 1055–1111] have shown the number of mapping class group lattice points intersecting a closed ball of radius R in Teichmüller space is asymptotic to ehR, where h is the dimension of the Teichmüller space. In contrast we show the number of Dehn twist lattice points intersecting a closed ball of radius
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General primitivity in the mapping class group J. Topol. Anal. (IF 0.8) Pub Date : 2023-12-14 Pankaj Kapari, Kashyap Rajeevsarathy
For g≥2, let Mod(Sg) be the mapping class group of the closed orientable surface Sg of genus g. In this paper, we obtain necessary and sufficient conditions under which a given pseudo-periodic mapping class can be a root of another up to conjugacy. Using this characterization, the canonical decomposition of (non-periodic) mapping classes, and some known algorithms, we give an algorithm for determining
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Real polynomials with constrained real divisors. I. Fundamental groups J. Topol. Anal. (IF 0.8) Pub Date : 2023-12-14 Gabriel Katz, Boris Shapiro, Volkmar Welker
In the late 80s, V. Arnold and V. Vassiliev initiated the topological study of the space of real univariate polynomials of a given degree d and with no real roots of multiplicity exceeding a given positive integer. Expanding their studies, we consider the spaces 𝒫dcΘ of real monic univariate polynomials of degree d whose real divisors avoid sequences of root multiplicities, taken from a given poset
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New examples in dimensions N ≥ 4 related to a question of J. W. Cannon and S. G. Wayment J. Topol. Anal. (IF 0.8) Pub Date : 2023-12-14 Olga Frolkina
Solving R. J. Daverman’s problem, V. S. Krushkal described sticky Cantor sets in ℝN for N≥4. Such sets cannot be isotoped off themselves by small ambient isotopies. Using Krushkal sets, we present a new series of wild embeddings related to a question of J. W. Cannon and S. G. Wayment (1970). Namely, for N≥4, we construct examples of compacta X⊂ℝN with the following two properties: some sequence {Xi⊂ℝN∖X
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Are two H-spaces homotopy equivalent? An algorithmic view point J. Topol. Anal. (IF 0.8) Pub Date : 2023-12-09 Mária Šimková
This paper proposes an algorithm that decides if two simply connected spaces represented by finite simplicial sets of finite k-type and finite dimension d are homotopy equivalent. If the spaces are homotopy equivalent, the algorithm finds a homotopy equivalence between their Postnikov stages in dimension d. As a consequence, we get an algorithm deciding if two spaces represented by finite simplicial
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Tomiyama’s K-commutative diagrams of minimal dynamical systems J. Topol. Anal. (IF 0.8) Pub Date : 2023-12-08 Sihan Wei
Let K be the Cantor space and 𝕊2n be an even-dimensional sphere. By applying a result of the existence of minimal skew products, we show that, associated with any Cantor minimal system (K,α), there is a class ℛ0(α̃) of minimal skew products on K×𝕊2n, such that for any two rigid homeomorphisms α∈ℛ0(α̃) and β∈ℛ0(β̃), the notions of approximate K-conjugacy and C∗-strongly approximate conjugacy coincide
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Maps from 3-manifolds to 4-manifolds that induce isomorphisms on π1 J. Topol. Anal. (IF 0.8) Pub Date : 2023-12-08 Hongbin Sun, Zhongzi Wang
In this paper, we prove that if a closed orientable 3-manifold M admits a map f:M→N to a closed orientable 4-manifold N such that f induces an isomorphism on fundamental groups, then M is homeomorphic to #kS1×S2 or S3. Relevant results on higher dimensional manifolds are also obtained.
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Remark on ordered braid groups J. Topol. Anal. (IF 0.8) Pub Date : 2023-11-27 Igor V. Nikolaev
We recover the Dehornoy order on the braid group B2g+n from the tracial state on a cluster C∗-algebra 𝔸(Sg,n) associated to the surface Sg,n of genus g with n boundary components. It is proved that the space of left-ordering of the fundamental group π1(Sg,n) is a totally disconnected dense subspace of the projective Teichmüller space ℙTg,n≅S6g−7+2n. In particular, each left-ordering of π1(Sg,n) defines
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Local Lagrangian Floer homology of quasi-minimally degenerate intersections J. Topol. Anal. (IF 0.8) Pub Date : 2023-11-15 Shamuel Auyeung
We define a broad class of local Lagrangian intersections which we call quasi-minimally degenerate (QMD) before developing techniques for studying their local Floer homology. In some cases, one may think of such intersections as modeled on minimally degenerate functions as defined by Kirwan. One major result of this paper is: if L0,L1 are two Lagrangian submanifolds whose intersection decomposes into
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The L2-torsion for representations of hyperbolic lattices J. Topol. Anal. (IF 0.8) Pub Date : 2023-10-19 Benjamin Waßermann
We prove equality of analytic and topological L2-torsion associated with an odd-dimensional finite volume hyperbolic manifold and a representation of the fundamental group which extends to the ambient Lie group. This generalizes a previous result due to Lück and Schick. Alternatively, this result can be regarded as the L2-analog of recent work by Müller and Rochon.
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Complete classification of generalized crossing changes between GOF-knots J. Topol. Anal. (IF 0.8) Pub Date : 2023-09-26 Kai Ishihara, Matt Rathbun
We analyze all monodromies of genus one fibered knots that possess clean or once-unclean arcs, and use this to determine all manifolds containing genus one fibered knots with generalized crossing changes resulting in another genus one fibered knot, and classify all such generalized crossing changes between two genus one, fibered knots.
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Finite index subgroups in Chevalley groups are bounded: An addendum to “On Bi-Invariant Word Metrics” J. Topol. Anal. (IF 0.8) Pub Date : 2023-09-07 Światosław R. Gal, Jarek Kȩdra, Alexander A. Trost
We prove that finite index subgroups in S-arithmetic Chevalley groups are bounded.
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Reeb flows with small contact volume and large return time to a global section J. Topol. Anal. (IF 0.8) Pub Date : 2023-09-05 Murat Sağlam
In this paper, we show that any co-oriented closed contact manifold of dimension at least five admits a contact form such that the contact volume is arbitrarily small but the Reeb flow admits a global hypersurface of section with the property that the minimal period on the boundary of the hypersurface and the first return time in the interior of the hypersurface are bounded below. An immediate consequence
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The ratio of homology rank to hyperbolic volume, I J. Topol. Anal. (IF 0.8) Pub Date : 2023-08-30 Rosemary K. Guzman, Peter B. Shalen
We show that for every finite-volume hyperbolic 3-manifold M and every prime p we have dimH1(M;Fp)<168.602⋅vol(M). There are slightly stronger estimates if p=2 or if M is non-compact. This improves on a result proved by Agol, Leininger and Margalit, which gave the same inequality with a coefficient of 334.08 in place of 168.602. It also improves on the analogous result with a coefficient of about 260
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Rigidity of mean convex subsets in non-negatively curved RCD spaces and stability of mean curvature bounds J. Topol. Anal. (IF 0.8) Pub Date : 2023-08-30 Christian Ketterer
We prove splitting theorems for mean convex open subsets in Riemannian curvature-dimension (RCD) spaces that extend results by Kasue et al. for Riemannian manifolds with boundary to a non-smooth setting. A corollary is for instance Frankel’s theorem. Then, we prove that our notion of mean curvature bounded from below for the boundary of an open subset is stable with respect to uniform convergence of
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Almost complex manifolds with total Betti number three J. Topol. Anal. (IF 0.8) Pub Date : 2023-08-25 Jiahao Hu
In this paper, we show the minimal total Betti number of a closed almost complex manifold of dimension 2n≥8 is four, thus confirming a conjecture of Sullivan except for dimension 6. Along the way, we prove the only simply connected closed complex manifold having total Betti number three is the complex projective plane.
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Homological eigenvalues of graph p-Laplacians J. Topol. Anal. (IF 0.8) Pub Date : 2023-08-25 Dong Zhang
Inspired by persistent homology in topological data analysis, we introduce the homological eigenvalues of the graph p-Laplacian Δp, which allows us to analyze and classify non-variational eigenvalues. We show the stability of homological eigenvalues, and we prove that for any homological eigenvalue λ(Δp), the function p↦p(2λ(Δp))1p is locally increasing, while the function p↦2−pλ(Δp) is locally decreasing
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Real tight contact structures on lens spaces and surface singularities J. Topol. Anal. (IF 0.8) Pub Date : 2023-08-03 Sinem Onaran, Ferit Ozturk
We give a partial classification for the real tight contact structures on solid tori up to equivariant contact isotopy and apply the results to the classification of real tight structures on S3 and real lens spaces L(p,±1). We prove that there is a unique real tight S3 and ℝP3. We show that there is at most one real tight L(p,±1) with respect to one of its two possible real structures. With respect
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Algebraic stability theorem for derived categories of zigzag persistence modules J. Topol. Anal. (IF 0.8) Pub Date : 2023-08-03 Yasuaki Hiraoka, Yuichi Ike, Michio Yoshiwaki
We study distances on zigzag persistence modules from the viewpoint of derived categories and Auslander–Reiten quivers. The derived category of ordinary persistence modules is derived equivalent to that of arbitrary zigzag persistence modules, depending on a classical tilting module. Through this derived equivalence, we define and compute distances on the derived category of arbitrary zigzag persistence
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Lower N-weighted Ricci curvature bound with 𝜀-range and displacement convexity of entropies J. Topol. Anal. (IF 0.8) Pub Date : 2023-08-03 Kazuhiro Kuwae, Yohei Sakurai
In this paper, we provide a characterization of a lower N-weighted Ricci curvature bound for N∈]−∞,1]∪[n,+∞] with 𝜀-range introduced by Lu–Minguzzi–Ohta [Comparison theorems on weighted Finsler manifolds and space-times with 𝜀-range, Anal. Geom. Metr. Spaces10(1) (2022) 1–30] in terms of a convexity of entropies over Wasserstein space. We further derive various interpolation inequalities and functional
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Numerical invariants for two-component virtual spatial graphs J. Topol. Anal. (IF 0.8) Pub Date : 2023-08-03 Komal Negi, Madeti Prabhakar
In this paper, we study two-component virtual spatial graphs, and define numerical invariants for the class of two-component virtual spatial graphs having some special conditions. These numerical invariants detect the non-amphichirality for this specific class of two component virtual spatial graphs. Further, we establish that one of these invariants is a Vassiliev type invariant.
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On the homology of spaces of equivariant maps J. Topol. Anal. (IF 0.8) Pub Date : 2023-08-02 V. A. Vassiliev
A spectral sequence calculating the homology groups of some spaces of maps equivariant under compact group actions is described. For the main motivating example, we calculate the rational homology groups of spaces of even and odd maps Sm→SM, m
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Fitting a manifold of large reach to noisy data J. Topol. Anal. (IF 0.8) Pub Date : 2023-07-28 Charles Fefferman, Sergei Ivanov, Matti Lassas, Hariharan Narayanan
Let ℳ⊂ℝn be a C2-smooth compact submanifold of dimension d. Assume that the volume of ℳ is at most V and the reach (i.e. the normal injectivity radius) of ℳ is greater than τ. Moreover, let μ be a probability measure on ℳ whose density on ℳ is a strictly positive Lipschitz-smooth function. Let xj∈ℳ, j=1,2,…,N be N independent random samples from distribution μ. Also, let ξj, j=1,2,…,N be independent
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Ribbon Yetter–Drinfeld modules and tangle invariants J. Topol. Anal. (IF 0.8) Pub Date : 2023-07-28 Kazuo Habiro, Yuka Kotorii
We define notions of pivotal and ribbon objects in a monoidal category. These constructions give pivotal or ribbon monoidal categories from a monoidal category which is not necessarily with duals. We apply this construction to the braided monoidal category of Yetter–Drinfeld modules over a Hopf algebra. This gives rise to the notion of ribbon Yetter–Drinfeld modules over a Hopf algebra, which form
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The ratio of homology rank to hyperbolic volume, II: The role of the Four Color Theorem J. Topol. Anal. (IF 0.8) Pub Date : 2023-07-28 Rosemary K. Guzman, Peter B. Shalen
Under mild topological restrictions, we obtain new linear upper bounds for the dimension of the mod p homology (for any prime p) of a finite-volume orientable hyperbolic 3-manifold M in terms of its volume. A surprising feature of the arguments in the paper is that they require an application of the Four Color Theorem. If M is closed, and either (a) π1(M) has no subgroup isomorphic to the fundamental
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On eigenvalues of geometrically finite hyperbolic manifolds of infinite volume J. Topol. Anal. (IF 0.8) Pub Date : 2023-07-28 Xiaolong Hans Han
Let M be an oriented geometrically finite hyperbolic manifold of infinite volume with dimension n≥3. For all k≥0, we provide a lower bound on the kth eigenvalue of the Laplace–Beltrami operator of M by a constant and the kth eigenvalue of some neighborhood of the thick part of the convex core. As an application, we recover a theorem similar to the one of Burger and Canary which bounds the bottom λ0
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The bounded isomorphism conjecture for box spaces of residually finite groups J. Topol. Anal. (IF 0.8) Pub Date : 2023-07-28 Markus Zeggel
In this paper we study a coarse version of the K-theoretic Farrell–Jones conjecture we call coarse or bounded isomorphism conjecture. Using controlled category theory we are able to translate this conjecture for asymptotically faithful covers into a more familiar form. This allows us to prove the conjecture for box spaces of residually finite groups whose Farrell–Jones assembly map with coefficients
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Linear isoperimetric inequality for homogeneous Hadamard manifolds J. Topol. Anal. (IF 0.8) Pub Date : 2023-07-28 Hjalti Isleifsson
It is well known that simply connected symmetric spaces of non-positive sectional curvature admit a linear isoperimetric filling inequality for cycles of dimension greater than or equal to the rank of the space. In this note, we extend that result to homogeneous Hadamard manifolds.
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Macroscopic scalar curvature and codimension 2 width J. Topol. Anal. (IF 0.8) Pub Date : 2023-07-24 Hannah Alpert, Alexey Balitskiy, Larry Guth
We show that a complete 3-dimensional Riemannian manifold M with finitely generated first homology has macroscopic dimension 1 if it satisfies the following “macroscopic curvature” assumptions: every ball of radius 10 in M has volume at most 4, and every loop in every ball of radius 1 in M is null-homologous in the concentric ball of radius 2.
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Chain flaring and L2-torsion of free-by-cyclic groups J. Topol. Anal. (IF 0.8) Pub Date : 2023-07-24 Matt Clay
We introduce a condition on the monodromy of a free-by-cyclic group, Gϕ, called the chain flare condition, that implies that the L2–torsion, ρ(2)(Gϕ), is nonzero. We conjecture that this condition holds whenever the monodromy is exponentially growing.
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Differential forms on orbifolds with corners J. Topol. Anal. (IF 0.8) Pub Date : 2023-07-24 Jake P. Solomon, Sara B. Tukachinsky
Motivated by symplectic geometry, we give a detailed account of differential forms and currents on orbifolds with corners, the pull-back and push-forward operations, and their fundamental properties. We work within the formalism where the category of orbifolds with corners is obtained as a localization of the category of étale proper groupoids with corners. Constructions and proofs are formulated in
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K-Theory of the maximal and reduced Roe algebras of metric spaces with A-by-CE coarse fibrations J. Topol. Anal. (IF 0.8) Pub Date : 2023-07-24 Liang Guo, Zheng Luo, Qin Wang, Yazhou Zhang
Let X be a discrete metric space with bounded geometry. In this paper, we show that if X admits an “A-by-CE” coarse fibration, then the canonical quotient map λ:Cmax∗(X)→C∗(X) from the maximal Roe algebra to the Roe algebra of X, and the canonical quotient map λ:Cu,max∗(X)→Cu∗(X) from the maximal uniform Roe algebra to the uniform Roe algebra of X, induce isomorphisms on K-theory. A typical example