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  • A few remarks on invariable generation in infinite groups
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-07-21
    Gil Goffer; Gennady A. Noskov

    A subset S of a group G invariably generates G if G is generated by {sg(s)|s∈S} for any choice of g(s)∈G,s∈S. A topological group G is said to be ℐ𝒢 if it is invariably generated by some subset S⊆G, and 𝒯ℐ𝒢 if it is topologically invariably generated by some subset S⊆G. In this paper, we study the problem of (topological) invariable generation for linear groups and for automorphism groups of trees

    更新日期:2020-08-05
  • Countable approximation of topological G-manifolds, II: linear Lie groups G
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-07-20
    Qayum Khan

    Let G be a matrix group. Topological G-manifolds with Palais-proper action have the G-homotopy type of countable G-CW complexes (3.2). This generalizes Elfving’s dissertation theorem for locally linear G-manifolds (1996). Also, we improve the Bredon–Floyd theorem from compact Lie groups G to arbitrary Lie groups G.

    更新日期:2020-07-24
  • Amenable covers and ℓ1-invisibility
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-07-20
    R. Frigerio

    Let X be a topological space admitting an amenable cover of multiplicity k∈ℕ. We show that, for every n≥k and every α∈Hn(X;ℝ), the image of α in the ℓ1-homology module Hnℓ1(X;ℝ) vanishes. This strengthens previous results by Gromov and Ivanov, who proved, under the same assumptions, that the ℓ1-seminorm of α vanishes.

    更新日期:2020-07-24
  • Separating subgroups of mapping class groups in homological representations
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-07-06
    Asaf Hadari

    Let Γ be either the mapping class group of a closed surface of genus ≥2, or the automorphism group of a free group of rank ≥3. Given any homological representation ρ of Γ corresponding to a finite cover, and any term ℐk of the Johnson filtration, we show that ρ(ℐk) has finite index in ρ(ℐ), the Torelli subgroup of Γ. Since [ℐ:ℐk]=∞ for k>1, this implies for instance that no such representation is faithful

    更新日期:2020-07-24
  • Projectively equivalent Finsler metrics on surfaces of negative Euler characteristic
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-06-19
    Julius Lang

    We prove that on a surface of negative Euler characteristic, two real-analytic Finsler metrics have the same unparametrized oriented geodesics, if and only if they differ by a scaling constant and addition of a closed 1-form.

    更新日期:2020-07-24
  • Symplectic Banach–Mazur distances between subsets of ℂn
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-04-18
    Michael Usher

    Following proposals of Ostrover and Polterovich, we introduce and study “coarse” and “fine” versions of a symplectic Banach–Mazur distance on certain open subsets of ℂn and other open Liouville domains. The coarse version declares two such domains to be close to each other if each domain admits a Liouville embedding into a slight dilate of the other; the fine version, which is similar to the distance

    更新日期:2020-04-18
  • A combinatorial model for the Menger curve
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-03-16
    Aristotelis Panagiotopoulos; Sławomir Solecki

    We represent the universal Menger curve as the topological realization |𝕄| of the projective Fraïssé limit 𝕄 of the class of all finite connected graphs. We show that 𝕄 satisfies combinatorial analogues of the Mayer–Oversteegen–Tymchatyn homogeneity theorem and the Anderson–Wilson projective universality theorem. Our arguments involve only 0-dimensional topology and constructions on finite graphs

    更新日期:2020-03-16
  • The Kasparov product on submersions of open manifolds
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-02-19
    Koen van den Dungen

    We study the Kasparov product on (possibly non-compact and incomplete) Riemannian manifolds. Specifically, we show on a submersion of Riemannian manifolds that the tensor sum of a regular vertically elliptic operator on the total space and an elliptic operator on the base space represents the Kasparov product of the corresponding classes in KK-theory. This construction works in general for symmetric

    更新日期:2020-02-19
  • The classification of certain ASH C*-algebras of real rank zero
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-02-18
    Qingnan An; George A. Elliott; Zhiqiang Li; Zhichao Liu

    In this paper, using ordered total K-theory, we give a K-theoretic classification for the real rank zero inductive limits of direct sums of generalized dimension drop interval algebras.

    更新日期:2020-02-18
  • Some spherical functions on hyperbolic groups
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-01-28
    Adrien Boyer

    We investigate properties of some spherical functions defined on hyperbolic groups using boundary representations on the Gromov boundary endowed with the Patterson–Sullivan measure class. We prove sharp decay estimates for spherical functions as well as spectral inequalities associated with boundary representations. This point of view on the boundary allows us to view the so-called property RD (also

    更新日期:2020-01-28
  • Double points in families of map germs from ℝ2 to ℝ3
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-01-28
    J. A. Moya-Pérez; J. J. Nuño-Ballesteros

    We show that a 1-parameter family of real analytic map germs ft:(ℝ2,0)→(ℝ3,0) with isolated instability is topologically trivial if it is excellent and the family of double point curves D(ft) in (ℝ2,0) is topologically trivial. In particular, we deduce that ft is topologically trivial when the Milnor number μ(D(ft)) is constant.

    更新日期:2020-01-28
  • Straightening warped cones
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-01-15
    Damian Sawicki; Jianchao Wu

    We provide the converses to two results of Roe [Warped cones and property A, Geom. Topol.9 (2005) 163–178, https://doi.org/10.2140/9t.2005.9.163]: first, the warped cone associated to a free action of an a-T-menable group admits a fibered coarse embedding into a Hilbert space, and second, a free action yielding a warped cone with property A must be amenable. We construct examples showing that in both

    更新日期:2020-01-15
  • The kernel of the monodromy of the universal family of degree d smooth plane curves
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-01-15
    Reid Monroe Harris

    We consider the parameter space 𝒰d of smooth plane curves of degree d. The universal smooth plane curve of degree d is a fiber bundle ℰd→𝒰d with fiber diffeomorphic to a surface Σg. This bundle gives rise to a monodromy homomorphism ρd:π1(𝒰d)→Mod(Σg), where Mod(Σg):=π0(Diff+(Σg)) is the mapping class group of Σg. The main result of this paper is that the kernel of ρ4:π1(𝒰4)→Mod(Σ3) is isomorphic

    更新日期:2020-01-15
  • Cohomology groups invariant under continuous orbit equivalence
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-01-08
    Yongle Jiang

    By the work of Brodzki–Niblo–Nowak–Wright and Monod, topological amenability of a continuous group action can be characterized using uniformly finite homology groups or bounded cohomology groups associated to this action. We show that (certain variations of) these groups are invariants for topologically free actions under continuous orbit equivalence.

    更新日期:2020-01-08
  • Separation profiles of graphs of fractals
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-01-07
    Valeriia Gladkova; Verna Shum

    We continue the exploration of the relationship between conformal dimension and the separation profile by computing the separation of families of spheres in hyperbolic graphs whose boundaries are standard Sierpiński carpets and Menger sponges. In all cases, we show that the separation of these spheres is nd−1d for some d which is strictly smaller than the conformal dimension, in contrast to the case

    更新日期:2020-01-07
  • Graph approximations to the Laplacian spectra
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-01-07
    Jinpeng Lu

    I prove that the spectrum of the Laplace–Beltrami operator with the Neumann boundary condition on a compact Riemannian manifold with boundary admits a fast approximation by the spectra of suitable graph Laplacians on proximity graphs on the manifold, and similar graph approximation works for metric-measure spaces glued out of compact Riemannian manifolds of the same dimension.

    更新日期:2020-01-07
  • Transgression in bounded cohomology and a conjecture of Monod
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-11-15
    Andreas Ott

    We develop an algebro-analytic framework for the systematic study of the continuous bounded cohomology of Lie groups in large degree. As an application, we examine the continuous bounded cohomology of PSL(2,ℝ) with trivial real coefficients in all degrees greater than two. We prove a vanishing result for strongly reducible classes, thus providing further evidence for a conjecture of Monod. On the cochain

    更新日期:2019-11-15
  • Random simplicial complexes, duality and the critical dimension
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-10-31
    Michael Farber; Lewis Mead; Tahl Nowik

    In this paper, we discuss two general models of random simplicial complexes which we call the lower and the upper models. We show that these models are dual to each other with respect to combinatorial Alexander duality. The behavior of the Betti numbers in the lower model is characterized by the notion of critical dimension, which was introduced by Costa and Farber in [Large random simplicial complexes

    更新日期:2019-10-31
  • Projective properties of Lorentzian surfaces
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-10-29
    Pierre Mounoud

    We investigate projective properties of Lorentzian surfaces. In particular, we prove that if T is a non-flat torus, then the index of its isometry group in its projective group is at most two. We also prove that any topologically finite non-compact surface can be endowed with a metric having a non-isometric projective transformation of infinite order.

    更新日期:2019-10-29
  • Mean action of periodic orbits of area-preserving annulus diffeomorphisms
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-10-29
    Morgan Weiler

    An area-preserving diffeomorphism of an annulus has an “action function” which measures how the diffeomorphism distorts curves. The average value of the action function over the annulus is known as the Calabi invariant of the diffeomorphism, while the average value of the action function over a periodic orbit of the diffeomorphism is the mean action of the orbit. If an area-preserving annulus diffeomorphism

    更新日期:2019-10-29
  • The isometric embedding problem for length metric spaces
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-10-02
    Barry Minemyer

    We prove that every proper n-dimensional length metric space admits an “approximate isometric embedding” into Lorentzian space ℝ3n+6,1. By an “approximate isometric embedding” we mean an embedding which preserves the energy functional on a prescribed set of geodesics connecting a dense set of points.

    更新日期:2019-10-02
  • Complexity of unknotting of trivial 2-knots
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-09-30
    Boris Lishak; Alexander Nabutovsky

    We construct a family of trivial 2-knots ki in ℝ4 such that the maximal complexity of 2-knots in any isotopy connecting ki with the standard unknot grows faster than a tower of exponentials of any fixed height of the complexity of ki. Here, we can either construct ki as smooth embeddings and measure their complexity as the ropelength (a.k.a the crumpledness) or construct PL-knots ki, consider isotopies

    更新日期:2019-09-30
  • Bubbling complex projective structures with quasi-Fuchsian holonomy
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-09-12
    Lorenzo Ruffoni

    For a given quasi-Fuchsian representation ρ:π1(S)→PSL2ℂ of the fundamental group of a closed surface S of genus g≥2, we prove that a generic branched complex projective structure on S with holonomy ρ and two branch points can be obtained from some unbranched structure on S with the same holonomy by bubbling, i.e. a suitable connected sum with a copy of ℂℙ1.

    更新日期:2019-09-12
  • Skinning bounds along thick rays
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-09-09
    Kenneth Bromberg; Autumn Kent; Yair Minsky

    We show that the diameter of the skinning map of an acylindrical hyperbolic 3-manifold M is bounded on 𝜀-thick Teichmüller geodesics by a constant depending only on 𝜀 and the topological type of ∂M.

    更新日期:2019-09-09
  • Dynamical complexity and K-theory of Lp operator crossed products
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-09-09
    Yeong Chyuan Chung

    We apply quantitative (or controlled) K-theory to prove that a certain Lp assembly map is an isomorphism for p∈[1,∞) when an action of a countable discrete group Γ on a compact Hausdorff space X has finite dynamical complexity. When p=2, this is a model for the Baum–Connes assembly map for Γ with coefficients in C(X), and was shown to be an isomorphism by Guentner et al.

    更新日期:2019-09-09
  • On the isomorphism problem for C∗-algebras of nilpotent Lie groups
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-09-02
    Ingrid Beltiţă; Daniel Beltiţă

    We investigate to what extent a nilpotent Lie group is determined by its C∗-algebra. We prove that, within the class of exponential Lie groups, direct products of Heisenberg groups with abelian Lie groups are uniquely determined even by their unitary dual, while nilpotent Lie groups of dimension ≤5 are uniquely determined by the Morita equivalence class of their C∗-algebras. We also find that this

    更新日期:2019-09-02
  • Bredon cohomological dimension for virtually abelian stabilisers for CAT(0) groups
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-08-28
    Tomasz Prytuła

    Given a discrete group G, for any integer r≥0 we consider the family of all virtually abelian subgroups of G of rank at most r. We give an upper bound for the Bredon cohomological dimension of G for this family for a certain class of groups acting on CAT(0) spaces. This covers the case of Coxeter groups, Right-angled Artin groups, fundamental groups of special cube complexes and graph products of finite

    更新日期:2019-08-28
  • Basic Dolbeault cohomology and Weitzenböck formulas on transversely Kähler foliations
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-08-20
    Seoung Dal Jung; Ken Richardson

    We study basic Dolbeault cohomology and find new Weitzenböck formulas on a transversely Kähler foliation. We investigate conditions on mean curvature and Ricci curvature that impose restrictions on basic Dolbeault cohomology. For example, we prove that on a transversely Kähler foliation with positive transversal Ricci curvature, there are no nonzero basic-harmonic forms of type (r,0), among other results

    更新日期:2019-08-20
  • The pointed intrinsic flat distance between locally integral current spaces
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-07-29
    Shu Takeuchi

    In this note, we define a distance between two pointed locally integral current spaces. We prove that a sequence of pointed locally integral current spaces converges with respect to this distance if and only if it converges in the sense of Lang–Wenger. This enables us to state the compactness theorem by Lang–Wenger for pointed locally integral current spaces in terms of a distance function.

    更新日期:2019-07-29
  • Harmonic spinors on the Davis hyperbolic 4-manifold
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-07-17
    John G. Ratcliffe; Daniel Ruberman; Steven T. Tschantz

    In this paper, we use the G-spin theorem to show that the Davis hyperbolic 4-manifold admits harmonic spinors. This is the first example of a closed hyperbolic 4-manifold that admits harmonic spinors. We also explicitly describe the spinor bundle of a spin hyperbolic 2- or 4-manifold and show how to calculated the subtle sign terms in the G-spin theorem for an isometry, with isolated fixed points,

    更新日期:2019-07-17
  • Abstract commensurators of surface groups
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-07-05
    Khalid Bou-Rabee; Daniel Studenmund

    Let Γ be the fundamental group of a surface of finite type and Comm(Γ) be its abstract commensurator. Then Comm(Γ) contains the solvable Baumslag–Solitar groups 〈a,b:aba−1=bn〉 for any n>1. Moreover, the Baumslag–Solitar group 〈a,b:ab2a−1=b3〉 has an image in Comm(Γ) that is not residually finite. Our proofs are computer-assisted. Our results also illustrate that finitely-generated subgroups of Comm(Γ)

    更新日期:2019-07-05
  • Inductive limit of direct sums of simple TAI algebras
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-06-27
    Bo Cui; Chunlan Jiang; Liangqing Li

    An ATAI (or ATAF, respectively) algebra, introduced in [C. Jiang, A classification of non simple C*-algebras of tracial rank one: Inductive limit of finite direct sums of simple TAI C*-algebras, J. Topol. Anal.3 (2011) 385–404] (or in [X. C. Fang, The classification of certain non-simple C*-algebras of tracial rank zero, J. Funct. Anal.256 (2009) 3861–3891], respectively) is an inductive limit limn→∞(An=⊕i=1Ani

    更新日期:2019-06-27
  • On the Cohomology of the Classifying Spaces of Projective Unitary Groups
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-06-16
    Xing Gu

    Let BPUn be the classifying space of PUn, the projective unitary group of order n, for n>1. We use a Serre spectral sequence to determine the ring structure of H∗(BPUn;ℤ) up to degree 10, as well as a family of distinguished elements of H2p+2(BPUn;ℤ), for each prime divisor p of n. We also study the primitive elements of H∗(BUn;ℤ) as a comodule over H∗(K(ℤ,2);ℤ), where the comodule structure is given

    更新日期:2019-06-16
  • Stability of exponentially harmonic maps
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-06-10
    Yuan-Jen Chiang

    We show that any stable exponentially harmonic map from a compact Riemannian manifold into a compact simply-connected δ-pinched Riemannian manifold under certain circumstance is constant in two different versions. We also prove that a non-constant exponentially harmonic map from a compact hypersurface into a compact Riemannian manifold satisfying certain condition is unstable.

    更新日期:2019-06-10
  • Fixed-point theorems for groups acting on non-positively curved manifolds
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-06-10
    Omer Lavy

    We study isometric actions of Steinberg groups on Hadamard manifolds. We prove some rigidity properties related to these actions. In particular, we show that every isometric action of Stn(𝔽p〈t1,…,tk〉) on Hadamard manifold when n≥3 factors through a finite quotient. We further study actions on infinite-dimensional manifolds and prove a fixed-point theorem related to such actions.

    更新日期:2019-06-10
  • Section problems for configuration spaces of surfaces
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-06-04
    Lei Chen

    In this paper, we give a close-to-sharp answer to the basic questions: When is there a continuous way to add a point to a configuration of n ordered points on a surface S of finite type so that all the points are still distinct? When this is possible, what are all the ways to do it? More precisely, let PConfn(S) be the space of ordered n-tuple of distinct points in S. Let fn(S):PConfn+1(S)→PConfn(S)

    更新日期:2019-06-04
  • Riemannian metrics and Laplacians for generalized smooth distributions
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-05-12
    Iakovos Androulidakis; Yuri Kordyukov

    We show that any generalized smooth distribution on a smooth manifold, possibly of non-constant rank, admits a Riemannian metric. Using such a metric, we attach a Laplace operator to any smooth distribution as such. When the underlying manifold is compact, we show that it is essentially self-adjoint. Viewing this Laplacian in the longitudinal pseudodifferential calculus of the smallest singular foliation

    更新日期:2019-05-12
  • Disjoint superheavy subsets and fragmentation norms
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-05-12
    Morimichi Kawasaki; Ryuma Orita

    We present a lower bound for a fragmentation norm and construct a bi-Lipschitz embedding I:ℝn→Ham(M) with respect to the fragmentation norm on the group Ham(M) of Hamiltonian diffeomorphisms of a symplectic manifold (M,ω). As an application, we provide an answer to Brandenbursky’s question on fragmentation norms on Ham(Σg), where Σg is a closed Riemannian surface of genus g≥2.

    更新日期:2019-05-12
  • Harmonic maps and wild Teichmüller spaces
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-05-06
    Subhojoy Gupta

    We use meromorphic quadratic differentials with higher order poles to parametrize the Teichmüller space of crowned hyperbolic surfaces. Such a surface is obtained on uniformizing a compact Riemann surface with marked points on its boundary components, and has noncompact ends with boundary cusps. This extends Wolf’s parametrization of the Teichmüller space of a closed surface using holomorphic quadratic

    更新日期:2019-05-06
  • Intersection space cohomology of three-strata pseudomanifolds
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-04-08
    J. Timo Essig

    The theory of intersection spaces assigns cell complexes to certain stratified topological pseudomanifolds depending on a perversity function in the sense of intersection homology. The main property of the intersection spaces is Poincaré duality over complementary perversities for the reduced singular (co)homology groups with rational coefficients. This (co)homology theory is not isomorphic to intersection

    更新日期:2019-04-08
  • Minimal surfaces in the three-dimensional sphere with high symmetry
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-04-08
    Sheng Bai; Chao Wang; Shicheng Wang

    Using the Lawson existence theorem of minimal surfaces and the symmetries of the Hopf fibration, we will construct symmetric embedded closed minimal surfaces in the three-dimensional sphere. These surfaces contain the Clifford torus, the Lawson’s minimal surfaces, and seven new minimal surfaces with genera 9, 25, 49, 121, 121, 361 and 841. We will also discuss the relation between such surfaces and

    更新日期:2019-04-08
  • Systolically extremal nonpositively curved surfaces are flat with finitely many singularities
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-04-08
    Mikhail G. Katz; Stéphane Sabourau

    The regularity of systolically extremal surfaces is a notoriously difficult problem already discussed by Gromov in 1983, who proposed an argument toward the existence of L2-extremizers exploiting the theory of r-regularity developed by White and others by the 1950s. We propose to study the problem of systolically extremal metrics in the context of generalized metrics of nonpositive curvature. A natural

    更新日期:2019-04-08
  • Conjugate words and intersections of geodesics in ℍ2
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-04-03
    Rita Gitik

    We investigate intersections of geodesic lines in ℍ2 and in an associated tree T, proving the following result. Let M be a punctured hyperbolic torus and let γ be a closed geodesic in M. Any edge of any triangle formed by distinct geodesic lines in the preimage of γ in ℍ2 is shorter than γ. However, a similar result does not hold in the tree T. Let W be a reduced and cyclically reduced word in π1(M)=〈x

    更新日期:2019-04-03
  • Minimal Penner dilatations on nonorientable surfaces
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-04-03
    Livio Liechti; Balázs Strenner

    For any nonorientable closed surface, we determine the minimal dilatation among pseudo-Anosov mapping classes arising from Penner’s construction. We deduce that the sequence of minimal Penner dilatations has exactly two accumulation points, in contrast to the case of orientable surfaces where there is only one accumulation point. One of our key techniques is representing pseudo-Anosov dilatations as

    更新日期:2019-04-03
  • Almost-automorphisms of trees, cloning systems and finiteness properties
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-03-24
    Rachel Skipper; Matthew C. B. Zaremsky

    We prove that the group of almost-automorphisms of the infinite rooted regular d-ary tree 𝒯d arises naturally as the Thompson-like group of a so-called d-ary cloning system. A similar phenomenon occurs for any Röver–Nekrashevych group Vd(G), for G≤Aut(𝒯d) a self-similar group. We use this framework to expand on work of Belk and Matucci, who proved that the Röver group, using the Grigorchuk group

    更新日期:2019-03-24
  • Group approximation in Cayley topology and coarse geometry Part I: Coarse embeddings of amenable groups
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-03-24
    Masato Mimura; Hiroki Sako

    The objective of this series is to study metric geometric properties of (coarse) disjoint unions of amenable Cayley graphs. We employ the Cayley topology and observe connections between large scale structure of metric spaces and group properties of Cayley accumulation points. In Part I, we prove that a disjoint union has property A of Yu if and only if all groups appearing as Cayley accumulation points

    更新日期:2019-03-24
  • Variations on the theme of the uniform boundary condition
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-03-24
    Daniel Fauser; Clara Löh

    The uniform boundary condition (UBC) in a normed chain complex asks for a uniform linear bound on fillings of null-homologous cycles. For the ℓ1-norm on the singular chain complex, Matsumoto and Morita established a characterization of the UBC in terms of bounded cohomology. In particular, spaces with amenable fundamental group satisfy the UBC in every degree. We will give an alternative proof of statements

    更新日期:2019-03-24
  • The space of relative orders and a generalization of Morris indicability theorem
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-03-11
    Yago Antolín; Cristóbal Rivas

    We introduce the space of relative orders on a group and show that it is compact whenever the group is finitely generated. We use this to show that if G is a finitely generated group acting on the line by order preserving homeomorphisms and some stabilizer of a point is a proper and co-amenable subgroup, then G surjects onto ℤ. This is a generalization of a theorem of Morris.

    更新日期:2019-03-11
  • The topology of Baumslag–Solitar representations
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-03-11
    Maxime Bergeron; Lior Silberman

    Let Γ=〈a,b|abpa−1=bq〉 be a Baumslag–Solitar group and let G be a complex reductive algebraic group with maximal compact subgroup K

    更新日期:2019-03-11
  • The Omega limit set of a family of chords
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-02-25
    Edward Belbruno; Urs Frauenfelder; Otto van Koert

    In this paper, we study the limit behavior of a family of chords on compact energy hypersurfaces of a family of Hamiltonians. Under the assumption that the energy hypersurfaces are all of contact type, we give results on the Omega limit set of this family of chords. Roughly speaking, such a family must either end in a degeneracy, in which case it joins another family, or can be continued. This gives

    更新日期:2019-02-25
  • Topological complexity of the work map
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-02-01
    Aniceto Murillo; Jie Wu

    We introduce the topological complexity of the work map associated to a robot system. In broad terms, this measures the complexity of any algorithm controlling, not just the motion of the configuration space of the given system, but the task for which the system has been designed. From a purely topological point of view, this is a homotopy invariant of a map which generalizes the classical topological

    更新日期:2019-02-01
  • How large isotopy is needed to connect homotopic diffeomorphisms (of 𝕋2)
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-01-22
    Dmitri Burago; Jinpeng Lu; Tristan Ozuch

    Given a diffeomorphism which is homotopic to the identity from the 2-torus to itself, we construct an isotopy whose norm is controlled by that of the diffeomorphism in question.

    更新日期:2019-01-22
  • The geometry of k-free hyperbolic 3-manifolds
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-01-14
    R. K. Guzman; P. B. Shalen

    We investigate the geometry of closed, orientable, hyperbolic 3-manifolds whose fundamental groups are k-free for a given integer k≥3. We show that any such manifold M contains a point P with the following property: If S is the set of elements of π1(M,P) represented by loops of length

    更新日期:2019-01-14
  • Algebraic intersection spaces
    J. Topol. Anal. (IF 0.817) Pub Date : 2018-12-09
    Christian Geske

    We define a variant of intersection space theory that applies to many compact complex and real analytic spaces X, including all complex projective varieties; this is a significant extension to a theory which has so far only been shown to apply to a particular subclass of spaces with smooth singular sets. We verify existence of these so-called algebraic intersection spaces and show that they are the

    更新日期:2018-12-09
  • S1-Equivariant bordism, invariant metrics of positive scalar curvature, and rigidity of elliptic genera
    J. Topol. Anal. (IF 0.817) Pub Date : 2018-11-28
    Michael Wiemeler

    We construct geometric generators of the effective S1-equivariant Spin- (and oriented) bordism groups with two inverted. We apply this construction to the question of which S1-manifolds admit invariant metrics of positive scalar curvature. It turns out that, up to taking connected sums with several copies of the same manifold, the only obstruction to the existence of such a metric is an Â-genus of

    更新日期:2018-11-28
  • Homologically trivial symplectic cyclic actions need not extend to Hamiltonian circle actions
    J. Topol. Anal. (IF 0.817) Pub Date : 2018-11-22
    River Chiang; Liat Kessler

    We give examples of symplectic actions of a cyclic group, inducing a trivial action on homology, on four-manifolds that admit Hamiltonian circle actions, and show that they do not extend to Hamiltonian circle actions. Our work applies holomorphic methods to extend combinatorial tools developed for circle actions to study cyclic actions.

    更新日期:2018-11-22
  • Compactifications of manifolds with boundary
    J. Topol. Anal. (IF 0.817) Pub Date : 2018-11-22
    Shijie Gu; Craig R. Guilbault

    This paper is concerned with compactifications of high-dimensional manifolds. Siebenmann’s iconic 1965 dissertation [L. C. Siebenmann, The obstruction to finding a boundary for an open manifold of dimension greater than five, Ph.D. thesis, Princeton Univ. (1965), MR 2615648] provided necessary and sufficient conditions for an open manifold Mm (m≥6) to be compactifiable by addition of a manifold boundary

    更新日期:2018-11-22
  • Twisted geometric K-homology for proper actions of discrete groups
    J. Topol. Anal. (IF 0.817) Pub Date : 2018-11-15
    Noé Bárcenas

    We define Twisted Equivariant K-homology groups using geometric cycles. We compare them with analytical approaches using Kasparov KK-theory and (twisted) C∗-algebras of groups and groupoids.

    更新日期:2018-11-15
  • A triple-point Whitney trick
    J. Topol. Anal. (IF 0.817) Pub Date : 2018-11-15
    Sergey A. Melikhov

    We use a triple-point version of the Whitney trick to show that ornaments of three orientable (2k−1)-manifolds in ℝ3k−1, k>2, are classified by the μ-invariant. A very similar (but not identical) construction was found independently by I. Mabillard and U. Wagner, who also made it work in a much more general situation and obtained impressive applications. The present note is, by contrast, focused on

    更新日期:2018-11-15
  • Coarse homology of leaves of foliations
    J. Topol. Anal. (IF 0.817) Pub Date : 2018-11-13
    Robert Schmidt

    We investigate the coarse homology of leaves in foliations of compact manifolds. This is motivated by the observation that the non-leaves constructed by Schweitzer and by Zeghib all have non-finitely generated coarse homology. This led us to ask whether the coarse homology of leaves in a compact manifold always has to be finitely generated. We show that this is not the case by proving that there exist

    更新日期:2018-11-13
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