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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
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Deficiency, relation gap and two-dimensional groups J. Topol. Anal. (IF 0.8) Pub Date : 2023-07-24 Aditi Kar, Nikolay Nikolov
Let G be a finitely presented, residually finite group and let δ(G) denote the deficiency of G. Assume that every subgroup H of finite index in G satisfies δ(H)−1=|G:H|(δ(G)−1). We conjecture that G has a two-dimensional finite classifying space K(G,1). This conjecture is motivated by an open question about the deficiency gradient of groups and their L2-Betti numbers. In this note, we relate this conjecture
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Quasimorphisms on surfaces and continuity in the Hofer norm J. Topol. Anal. (IF 0.8) Pub Date : 2023-07-24 Michael Khanevsky
There are a number of known constructions of quasimorphisms on Hamiltonian groups. We show that on surfaces many of these quasimorphisms are not compatible with the Hofer norm in a sense they are not continuous and not Lipschitz. The only exception known to the author is the Calabi quasimorphism on a sphere [M. Entov and L. Polterovich, Calabi quasimorphism and quantum homology, Int. Math. Res. Not
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On permanence of regularity properties J. Topol. Anal. (IF 0.8) Pub Date : 2023-07-24 Hyun Ho Lee, Hiroyuki Osaka
We study a pair of C∗-algebras (A,B) by associating a ∗-homomorphism from A to B which allows an approximate left inverse to the ultrapower C∗-algebra of A as a completely positive map of order zero and show that important regularity properties related to the Elliott program pass from B to A in our setting.
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Nilpotent elements in the cohomology of the classifying space of a connected Lie group J. Topol. Anal. (IF 0.8) Pub Date : 2023-07-24 Masaki Kameko
We give an example of a compact connected Lie group of the lowest rank such that the mod 2 cohomology ring of its classifying space has a nonzero nilpotent element.
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Quantum speed limit and categorical energy relative to microlocal projector J. Topol. Anal. (IF 0.8) Pub Date : 2023-07-24 Sheng-Fu Chiu
Inspired by recent developments of quantum speed limit we introduce a categorical energy of sheaves in the derived category over a manifold relative to a microlocal projector. We utilize the tool of algebraic microlocal analysis to show that with regard to the microsupports of sheaves, our categorical energy gives a lower bound of the Hofer displacement energy. We also prove that on the other hand
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Simplicial volume of closed locally homogeneous Riemannian manifolds J. Topol. Anal. (IF 0.8) Pub Date : 2023-07-24 Peng Hui How
In this paper, we show that every closed, locally homogeneous Riemannian manifold with positive simplicial volume must be homeomorphic to a locally symmetric space of non-compact type, giving a converse to a result by Lafont and Schmidt within the scope of closed, locally homogeneous Riemannian manifolds. This characterizes all closed locally homogeneous Riemannian manifolds with nonzero simplicial
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Trees meet octahedron comparison J. Topol. Anal. (IF 0.8) Pub Date : 2023-07-24 Nina Lebedeva, Anton Petrunin
We show that metric trees and their products meet the octahedron comparison, which is a certain six-point metric comparison similar to Alexandrov’s CAT(0) comparison.
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Volumes of fibered 2-fold branched covers of 3-manifolds J. Topol. Anal. (IF 0.8) Pub Date : 2023-07-22 Susumu Hirose, Efstratia Kalfagianni, Eiko Kin
In this paper, we prove that for any closed, connected, oriented 3-manifold M, there exists an infinite family of 2-fold branched covers of M that are hyperbolic 3-manifolds and surface bundles over the circle with arbitrarily large volume.
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On symplectic capacities and their blind spots J. Topol. Anal. (IF 0.8) Pub Date : 2023-06-08 Ely Kerman, Yuanpu Liang
In this paper, we settle three basic questions concerning the Gutt–Hutchings capacities from [11] which are conjecturally equal to the Ekeland–Hofer capacities from [7, 8]. Our primary result settles a version of the recognition question from [4], in the negative. We prove that the Gutt–Hutchings capacities together with the volume do not constitute a complete set of symplectic invariants for star-shaped
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Characterizations of B-valued concentration inequalities via the Rademacher type J. Topol. Anal. (IF 0.8) Pub Date : 2023-06-07 Lixin Cheng, Wuyi He, Sijie Luo
In this paper, we show that a sufficient and necessary condition for that the Hoeffding concentration inequality of Banach space-valued (B-valued, for simplicity) random variables holds is that the Banach space in question admits the Rademacher type p for some 1≤p≤2; which is equivalent to that the Bernstein concentration inequality holds for such B-valued random variables. This is done by applying
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Systolic inequalities for the number of vertices J. Topol. Anal. (IF 0.8) Pub Date : 2023-03-01 Sergey Avvakumov, Alexey Balitskiy, Alfredo Hubard, Roman Karasev
Inspired by the classical Riemannian systolic inequality of Gromov, we present a combinatorial analogue providing a lower bound on the number of vertices of a simplicial complex in terms of its edge-path systole. Similarly to the Riemannian case, where the inequality holds under a topological assumption of “essentiality”, our proofs rely on a combinatorial analogue of that assumption. Under a stronger
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Extending periodic maps on surfaces over the 4-sphere J. Topol. Anal. (IF 0.8) Pub Date : 2022-11-30 Shicheng Wang, Zhongzi Wang
Let Fg be the closed orientable surface of genus g. We address the problem to extend torsion elements of the mapping class group ℳ(Fg) over the 4-sphere S4. Let wg be a torsion element of maximum order in ℳ(Fg). Results including: (1) For each g, wg is periodically extendable over S4 for some non-smooth embedding e:Fg→S4, and not periodically extendable over S4 for any smooth embedding e:Fg→S4. (2)
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Algebraic stability theorem for derived categories of zigzag persistence modules J. Topol. Anal. (IF 0.8) Pub Date : 2022-07-29 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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Lagrangian cobordisms in Liouville manifolds J. Topol. Anal. (IF 0.8) Pub Date : 2022-04-18 Valentin Bosshard
Floer theory for Lagrangian cobordisms was developed by Biran and Cornea in a series of papers [Lagrangian cobordism. I, J. Amer. Math. Soc. 26 (2013) 295–340; Lagrangian cobordism and Fukaya categories, Geom. Funct. Anal. 24 (2014) 1731–1830; Cone-decompositions of Lagrangian cobordisms in Lefschetz fibrations, Selecta Math. 23 (2017) 2635–2704] to study the triangulated structure of the derived Fukaya
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Largest hyperbolic actions and quasi-parabolic actions in groups J. Topol. Anal. (IF 0.8) Pub Date : 2022-03-12 Carolyn R. Abbott, Alexander J. Rasmussen
The set of equivalence classes of cobounded actions of a group on different hyperbolic metric spaces carries a natural partial order. The resulting poset thus gives rise to a notion of the “best” hyperbolic action of a group as the largest element of this poset, if such an element exists. We call such an action a largest hyperbolic action. While hyperbolic groups admit the largest hyperbolic actions
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Measured expanders J. Topol. Anal. (IF 0.8) Pub Date : 2022-03-12 Kang Li, Ján Špakula, Jiawen Zhang
By measured graphs, we mean graphs endowed with a measure on the set of vertices. In this context, we explore the relations between the appropriate Cheeger constant and Poincaré inequalities. We prove that the so-called Cheeger inequality holds in two cases: when the measure comes from a random walk, or when the measure has a bounded measure ratio. Moreover, we also prove that our measured (asymptotic)
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Divergent coindex sequence for dynamical systems J. Topol. Anal. (IF 0.8) Pub Date : 2022-03-08 Ruxi Shi, Masaki Tsukamoto
When a finite group freely acts on a topological space, we can define its index and coindex. They roughly measure the size of the given action. We explore the interaction between this index theory and topological dynamics. Given a fixed-point free dynamical system, the set of p-periodic points admits a natural free action of ℤ/pℤ for each prime number p. We are interested in the growth of its index
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Identities for hyperconvex Anosov representations J. Topol. Anal. (IF 0.8) Pub Date : 2022-03-08 Yan Mary He
In this paper, we establish Basmajian’s identity for certain (1,1,2)-hyperconvex Anosov representations from a free group into PGL(n, ℝ). We then study our series identities on holomorphic families of Cantor non-conformal repellers associated to complex (1,1,2)-hyperconvex Anosov representations. We show that the series is absolutely summable if the Hausdorff dimension of the Cantor set is strictly
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Lorentzian distance functions in contact geometry J. Topol. Anal. (IF 0.8) Pub Date : 2022-03-08 Jakob Hedicke
An important tool to analyse the causal structure of a Lorentzian manifold is given by the Lorentzian distance function. We define a class of Lorentzian distance functions on the group of contactomorphisms of a closed contact manifold depending on the choice of a contact form. These distance functions are continuous with respect to the Hofer norm for contactomorphisms defined by Shelukhin [The Hofer
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Enhanced Bounds for rho-invariants for both general and spherical 3-manifolds J. Topol. Anal. (IF 0.8) Pub Date : 2022-02-26 Geunho Lim
We establish enhanced bounds on Cheeger–Gromov ρ-invariants for general 3-manifolds and yet stronger bounds for special classes of 3-manifold. As key ingredients, we construct chain null-homotopies whose complexity is linearly bounded by its boundary. This result can be regarded as an algebraic topological analogue of Gromov’s conjecture for quantitative topology. The author hopes for applications
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Borel invariant for measurable cocycles of 3-manifold groups J. Topol. Anal. (IF 0.8) Pub Date : 2022-02-16 A. Savini
We introduce the notion of pullback along a measurable cocycle and we use it to extend the Borel invariant studied by Bucher, Burger and Iozzi to the world of measurable cocycles. The Borel invariant is constant along cohomology classes and has bounded absolute value. This allows to define maximal cocycles. We conclude by proving that maximal cocycles are actually trivializable to the restriction of
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Strata separation for the Weil–Petersson completion and gradient estimates for length functions J. Topol. Anal. (IF 0.8) Pub Date : 2022-01-19 Martin Bridgeman, Kenneth Bromberg
In general, it is difficult to measure distances in the Weil–Petersson metric on Teichmüller space. Here we consider the distance between strata in the Weil–Petersson completion of Teichmüller space of a surface of finite type. Wolpert showed that for strata whose closures do not intersect, there is a definite separation independent of the topology of the surface. We prove that the optimal value for
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Exhausting curve complexes by finite rigid sets on nonorientable surfaces J. Topol. Anal. (IF 0.8) Pub Date : 2022-01-12 Elmas Irmak
Let N be a compact, connected, nonorientable surface of genus g with n boundary components. Let 𝒞(N) be the curve complex of N. We prove that if (g,n) = (3, 0) or g + n ≥ 5, then there is an exhaustion of 𝒞(N) by a sequence of finite rigid sets. This improves the author’s result on exhaustion of 𝒞(N) by a sequence of finite superrigid sets.
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Linear fractional group as Galois group J. Topol. Anal. (IF 0.8) Pub Date : 2022-01-07 Lokenath Kundu
We compute all signatures of PSL2(𝔽7) and PSL2(𝔽11) which classify all orientation preserving actions of the groups PSL2(𝔽7) and PSL2(𝔽11) on compact, connected, orientable surfaces with orbifold genus ≥0. This classification is well-grounded in the other branches of Mathematics like topology, smooth and conformal geometry, algebraic categories, and it is also directly related to the inverse Galois
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The weak form of Hirzebruch’s prize question via rational surgery J. Topol. Anal. (IF 0.8) Pub Date : 2022-01-04 Aleksandar Milivojević
We present a relatively elementary construction of a spin manifold with vanishing first rational Pontryagin class satisfying the conditions of Hirzebruch’s prize question, using a modification of Sullivan’s theorem for the realization of rational homotopy types by closed smooth manifolds. As such this is an alternative to the solutions of the problem given by Hopkins–Mahowald, though without the guarantee
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Hilbert bundles with ends J. Topol. Anal. (IF 0.8) Pub Date : 2021-12-31 Tsuyoshi Kato, Daisuke Kishimoto, Mitsunobu Tsutaya
Given a countable metric space, we can consider its end. Then a basis of a Hilbert space indexed by the metric space defines an end of the Hilbert space, which is a new notion and different from an end as a metric space. Such an indexed basis also defines unitary operators of finite propagation, and these operators preserve an end of a Hilbert space. Then, we can define a Hilbert bundle with end, which
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Homologically visible closed geodesics on complete surfaces J. Topol. Anal. (IF 0.8) Pub Date : 2021-12-31 Simon Allais, Tobias Soethe
In this paper, we give multiple situations when having one or two geometrically distinct closed geodesics on a complete Riemannian cylinder, a complete Möbius band or a complete Riemannian plane leads to having infinitely many geometrically distinct closed geodesics. In particular, we prove that any complete cylinder with isolated closed geodesics has zero, one or infinitely many homologically visible
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Morse–Bott theory on posets and a homological Lusternik–Schnirelmann theorem J. Topol. Anal. (IF 0.8) Pub Date : 2021-12-30 D. Fernández-Ternero, E. Macías-Virgós, D. Mosquera-Lois, J. A. Vilches
We develop Morse–Bott theory on posets, generalizing both discrete Morse–Bott theory for regular complexes and Morse theory on posets. Moreover, we prove a Lusternik–Schnirelmann theorem for general matchings on posets, in particular, for Morse–Bott functions.
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The coordinate algebra of a quantum symplectic sphere does not embed into any C*-algebra J. Topol. Anal. (IF 0.8) Pub Date : 2021-12-02 Francesco D’Andrea, Giovanni Landi
In this note, we generalize a result of Mikkelsen–Szymański and show that, for every n≥2, any bounded ∗-representation of the quantum symplectic sphere Sq4n−1 annihilates the first n−1 generators. We then classify irreducible representations of its coordinate algebra 𝒜(Sq4n−1).
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The coordinate algebra of a quantum symplectic sphere does not embed into any C*-algebra J. Topol. Anal. (IF 0.8) Pub Date : 2021-12-02 Francesco D’Andrea, Giovanni Landi
In this note, we generalize a result of Mikkelsen–Szymański and show that, for every n≥2, any bounded ∗-representation of the quantum symplectic sphere Sq4n−1 annihilates the first n − 1 generators. We then classify irreducible representations of its coordinate algebra 𝒜(Sq4n−1).
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Fukaya A∞-structures associated to Lefschetz fibrations. V J. Topol. Anal. (IF 0.8) Pub Date : 2021-11-29 Paul Seidel
We (re)consider how the Fukaya category of a Lefschetz fibration is related to that of the fiber. The distinguishing feature of the approach here is a more direct identification of the bimodule homomorphism involved.
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Coronas for properly combable spaces J. Topol. Anal. (IF 0.8) Pub Date : 2021-11-26 Alexander Engel, Christopher Wulff
This paper is a systematic approach to the construction of coronas (i.e. Higson dominated boundaries at infinity) of combable spaces. We introduce three additional properties for combings: properness, coherence and expandingness. Properness is the condition under which our construction of the corona works. Under the assumption of coherence and expandingness, attaching our corona to a Rips complex construction
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Effectual topological complexity J. Topol. Anal. (IF 0.8) Pub Date : 2021-11-24 Natalia Cadavid-Aguilar, Jesús González, Bárbara Gutiérrez, Cesar A. Ipanaque-Zapata
We introduce the effectual topological complexity (ETC) of a G-space X. This is a G-equivariant homotopy invariant sitting in between the effective topological complexity of the pair (X,G) and the (regular) topological complexity of the orbit space X/G. We study ETC for spheres and surfaces with antipodal involution, obtaining a full computation in the case of the torus. This allows us to prove the
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Hecke operators in Bredon (co)homology, K-(co)homology and Bianchi groups J. Topol. Anal. (IF 0.8) Pub Date : 2021-11-20 David Muñoz, Jorge Plazas, Mario Velásquez
In this paper, we provide a framework for the study of Hecke operators acting on the Bredon (co)homology of an arithmetic discrete group. Our main interest lies in the study of Hecke operators for Bianchi groups. Using the Baum–Connes conjecture, we can transfer computations in Bredon homology to obtain a Hecke action on the K-theory of the reduced C∗-algebra of the group. We show the power of this
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Formal aspects of parametrized topological complexity and its pointed version J. Topol. Anal. (IF 0.8) Pub Date : 2021-11-17 J. M. García-Calcines
The notion of parametrized topological complexity, introduced by Cohen, Farber and Weinberger, is extended to fiberwise spaces which are not necessarily Hurewicz fibrations. After exploring some formal properties of this extension we also introduce the pointed version of parametrized topological complexity. Finally, we give sufficient conditions so that both notions agree.
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Commutativity of the Haagerup tensor product and base change for operator modules J. Topol. Anal. (IF 0.8) Pub Date : 2021-11-15 Tyrone Crisp
By computing the completely bounded norm of the flip map on the Haagerup tensor product C0Y1⊗C0XC0Y2 associated to a pair of continuous mappings of locally compact Hausdorff spaces Y1→X←Y2, we establish a simple characterization of the Beck-Chevalley condition for base change of operator modules over commutative C∗-algebras, and a descent theorem for continuous fields of Hilbert spaces.
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Expanders and right-angled Artin groups J. Topol. Anal. (IF 0.8) Pub Date : 2021-11-13 Ramón Flores, Delaram Kahrobaei, Thomas Koberda
The purpose of this paper is to give a characterization of families of expander graphs via right-angled Artin groups. We prove that a sequence of simplicial graphs {Γi}i∈ℕ forms a family of expander graphs if and only if a certain natural mini-max invariant arising from the cup product in the cohomology rings of the groups {A(Γi)}i∈ℕ agrees with the Cheeger constant of the sequence of graphs, thus
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On the Hofer girth of the sphere of great circles J. Topol. Anal. (IF 0.8) Pub Date : 2021-10-30 Itamar Rosenfeld Rauch
An oriented equator of 𝕊2 is the image of an oriented embedding 𝕊1↪𝕊2 such that it divides 𝕊2 into two equal area halves. Following Chekanov, we define the Hofer distance between two oriented equators as the infimal Hofer norm of a Hamiltonian diffeomorphism taking one to another. Consider 𝜖q+ the space of oriented equators. We define the Hofer girth of an embedding j:𝕊2↪𝜖q+ as the infimum of
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Periodic solutions of Hilbert’s fourth problem J. Topol. Anal. (IF 0.8) Pub Date : 2021-10-22 J. C. Álvarez Paiva, J. Barbosa Gomes
It is shown that a possibly irreversible C2 Finsler metric on the torus, or on any other compact Euclidean space form, whose geodesics are straight lines is the sum of a flat metric and a closed 1-form. This is used to prove that if (M,g) is a compact Riemannian symmetric space of rank greater than one and F is a reversibleC2 Finsler metric on M whose unparametrized geodesics coincide with those of
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On geodesically reversible Finsler manifolds J. Topol. Anal. (IF 0.8) Pub Date : 2021-10-25 Yong Fang
A Finsler manifold is said to be geodesically reversible if the reversed curve of any geodesic remains a geometrical geodesic. Well-known examples of geodesically reversible Finsler metrics are Randers metrics with closed 1-forms. Another family of well-known examples are projectively flat Finsler metrics on the 2-sphere that have constant positive curvature. In this paper, we prove some geometrical
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Periodic solutions of Hilbert’s fourth problem J. Topol. Anal. (IF 0.8) Pub Date : 2021-10-22 J. C. Álvarez Paiva, J. Barbosa Gomes
It is shown that a possibly irreversible C2 Finsler metric on the torus, or on any other compact Euclidean space form, whose geodesics are straight lines is the sum of a flat metric and a closed 1-form. This is used to prove that if (M,g) is a compact Riemannian symmetric space of rank greater than one and F is a reversible C2 Finsler metric on M whose unparametrized geodesics coincide with those of
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On horizontal immersions of discs in fat distributions of type (4,6) J. Topol. Anal. (IF 0.8) Pub Date : 2021-10-09 Aritra Bhowmick
In this paper, we discuss horizontal immersions of discs in certain corank-2 fat distributions on 6-dimensional manifolds. The underlying real distribution of a holomorphic contact distribution on a complex 3 manifold belongs to this class. The main result presented here says that the associated nonlinear PDE is locally invertible. Using this we prove the existence of germs of embedded horizontal discs
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Complete 3-dimensional λ-translators in the Euclidean space ℝ4 J. Topol. Anal. (IF 0.8) Pub Date : 2021-10-09 Zhi Li, Guoxin Wei, Gangyi Chen
In this paper, we obtain the classification theorems for 3-dimensional complete λ-translators x:M3 → ℝ4 with constant squared norm S of the second fundamental form and constant f4 in the Euclidean space ℝ4.
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Cusp cobordism group of Morse functions J. Topol. Anal. (IF 0.8) Pub Date : 2021-10-06 Dominik J. Wrazidlo
By a Morse function on a compact manifold with boundary we mean a real-valued function without critical points near the boundary such that its critical points as well as the critical points of its restriction to the boundary are all nondegenerate. For such Morse functions, Saeki and Yamamoto have previously defined a certain notion of cusp cobordism, and computed the unoriented cusp cobordism group
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Normal subgroups of SimpHAtic groups J. Topol. Anal. (IF 0.8) Pub Date : 2021-10-06 Damian Osajda
A group is SimpHAtic if it acts geometrically on a simply connected simplicially hereditarily aspherical (SimpHAtic) complex. We show that finitely presented normal subgroups of the SimpHAtic groups are either: finite, or of finite index, or virtually free. This result applies, in particular, to normal subgroups of systolic groups. We prove similar strong restrictions on group extensions for other