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  • Extreme nonuniqueness of end-sum
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-12-11
    Jack S. Calcut; Craig R. Guilbault; Patrick V. Haggerty

    We give explicit examples of pairs of one-ended, open 4-manifolds whose end-sums yield uncountably many manifolds with distinct proper homotopy types. This answers strongly in the affirmative a conjecture of Siebenmann regarding nonuniqueness of end-sums. In addition to the construction of these examples, we provide a detailed discussion of the tools used to distinguish them; most importantly, the

    更新日期:2020-12-13
  • Banach–Mazur stability of von Neumann algebras
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-12-11
    Jean Roydor

    We initiate the study of perturbation of von Neumann algebras relatively to the Banach–Mazur distance. We first prove that the type decomposition is continuous, i.e. if two von Neumann algebras are close, then their respective summands of each type are close. We then prove that, under some vanishing conditions on its Hochschild cohomology groups, a von Neumann algebra is Banach–Mazur stable, i.e. any

    更新日期:2020-12-13
  • Example of a nontrivial irreducible geodesic net in the plane
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-12-11
    Fabian Parsch

    We construct a geodesic net in the plane with four unbalanced (boundary) vertices that has sixteen balanced vertices and does not contain nontrivial subnets. This is the first example of an irreducible geodesic net in the Euclidean plane with four boundary vertices that contain cycles of balanced vertices.

    更新日期:2020-12-13
  • Equivariant Benjamini–Schramm convergence of simplicial complexes and ℓ2-multiplicities
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-12-03
    Steffen Kionke; Michael Schrödl-Baumann

    We define a variant of Benjamini–Schramm convergence for finite simplicial complexes with the action of a fixed finite group G which leads to the notion of unimodular random rooted simplicial G-complexes. For every unimodular random rooted simplicial G-complex we define a corresponding ℓ2-homology and the ℓ2-multiplicity of an irreducible representation of G in the homology. The ℓ2-multiplicities generalize

    更新日期:2020-12-03
  • Q-Series and quantum spin networks
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-11-26
    Mohamed Elhamdadi; Mustafa Hajij; Jesse S. F. Levitt

    The tail of a quantum spin network in the two-sphere is a q-series associated to the network. We study the existence of the head and tail functions of quantum spin networks colored by 2n. We compute the q-series for an infinite family of quantum spin networks and give the relation between the tail of these networks and the tail of the colored Jones polynomial. Finally, we show that the family of quantum

    更新日期:2020-11-27
  • A nonlinear Lazarev–Lieb theorem: L2-orthogonality via motion planning
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-11-21
    Florian Frick; Matt Superdock

    Lazarev and Lieb showed that finitely many integrable functions from the unit interval to ℂ can be simultaneously annihilated in the L2 inner product by a smooth function to the unit circle. Here, we answer a question of Lazarev and Lieb proving a generalization of their result by lower bounding the equivariant topology of the space of smooth circle-valued functions with a certain W1,1-norm bound.

    更新日期:2020-11-23
  • Conjugation curvature for Cayley graphs
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-11-21
    Assaf Bar-Natan; Moon Duchin; Robert Kropholler

    We introduce a notion of Ricci curvature for Cayley graphs that can be thought of as “medium-scale” because it is neither infinitesimal nor asymptotic, but based on a chosen finite radius parameter. We argue that it gives the foundation for a definition of Ricci curvature well adapted to geometric group theory, beginning by observing that the sign can easily be characterized in terms of conjugation

    更新日期:2020-11-23
  • Braid group and leveling of a knot
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-11-21
    Sangbum Cho; Yuya Koda; Arim Seo

    Any knot K in genus-11-bridge position can be moved by isotopy to lie in a union of n parallel tori tubed by n−1 tubes so that K intersects each tube in two spanning arcs, which we call a leveling of the position. The minimal n for which this is possible is an invariant of the position, called the level number. In this work, we describe the leveling by the braid group on two points in the torus, which

    更新日期:2020-11-23
  • Matrix group actions on product of spheres
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-11-16
    Shengkui Ye

    Let SLn(ℤ) be the special linear group over integers and Mr=Sr1×Sr2,Tr1×Sr2, or Tr0×Sr1×Sr2, products of spheres and tori. We prove that any group action of SLn(ℤ) on Mr by diffeomorphims or piecewise linear homeomorphisms is trivial if r

    更新日期:2020-11-18
  • Coarse compactifications and controlled products
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-11-16
    Tomohiro Fukaya; Shin-ichi Oguni; Takamitsu Yamauchi

    We introduce the notion of controlled products on metric spaces as a generalization of Gromov products, and construct boundaries by using controlled products, which we call the Gromov boundaries. It is shown that the Gromov boundary with respect to a controlled product on a proper metric space is the ideal boundary of a coarse compactification of the space. It is also shown that there is a bijective

    更新日期:2020-11-18
  • Bridge trisections in rational surfaces
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-11-12
    Peter Lambert-Cole; Jeffrey Meier

    We study smooth isotopy classes of complex curves in complex surfaces from the perspective of the theory of bridge trisections, with a special focus on curves in ℂℙ2 and ℂℙ1×ℂℙ1. We are especially interested in bridge trisections and trisections that are as simple as possible, which we call efficient. We show that any curve in ℂℙ2 or ℂℙ1×ℂℙ1 admits an efficient bridge trisection. Because bridge trisections

    更新日期:2020-11-13
  • Local index theory for operators associated with Lie groupoid actions
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-11-12
    Denis Perrot

    We develop a local index theory for a class of operators associated with non-proper and non-isometric actions of Lie groupoids on smooth submersions. Such actions imply the existence of a short exact sequence of algebras, relating these operators to their non-commutative symbol. We then compute the connecting map induced by this extension on periodic cyclic cohomology. When cyclic cohomology is localized

    更新日期:2020-11-13
  • Duality systems of groups and PD(n)-systems of groups
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-11-12
    Rita Gitik

    We define a system of groups, a duality system of groups and a PD(n)-system of groups, generalizing the corresponding concepts of pairs of groups. We give several characterizations of duality systems of groups and apply these results to derive an important characterization of PD(n)-systems of groups.

    更新日期:2020-11-13
  • On macroscopic dimension of non-spin 4-manifolds
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-11-07
    Michelle Daher; Alexander Dranishnikov

    We prove that for 4-manifolds M with residually finite fundamental group and non-spin universal covering M̃, the inequality dimmcM̃≤3 implies the inequality dimmcM̃≤2. This allows us to complete the proof of Gromov’s Conjecture for 4-manifolds with abelian fundamental group.

    更新日期:2020-11-09
  • Lehmer’s problem for arbitrary groups
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-11-03
    W. Lück

    We consider the problem whether for a group G there exists a constant Λ(G)>1 such that for any (r,s)-matrix A over the integral group ring ℤG the Fuglede–Kadison determinant of the G-equivariant bounded operator L2(G)r→L2(G)s given by right multiplication with A is either one or greater or equal to Λ(G). If G is the infinite cyclic group and we consider only r=s=1, this is precisely Lehmer’s problem

    更新日期:2020-11-03
  • Generating the twist subgroup by involutions
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-10-19
    Tüli̇n Altunöz; Mehmetci̇k Pamuk; Oguz Yildiz

    For a nonorientable surface, the twist subgroup is an index 2 subgroup of the mapping class group generated by Dehn twists about two-sided simple closed curves. In this paper, we consider involution generators of the twist subgroup and give generating sets of involutions with smaller number of generators than the ones known in the literature using new techniques for finding involution generators.

    更新日期:2020-10-21
  • Relative hyperbolicity for automorphisms of free products and free groups
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-10-06
    François Dahmani; Ruoyu Li

    We prove that for a free product G with free factor system 𝒢, any automorphism ϕ preserving 𝒢, atoroidal (in a sense relative to 𝒢) and none of whose power send two different conjugates of subgroups in 𝒢 on conjugates of themselves by the same element, gives rise to a semidirect product G⋊ϕℤ that is relatively hyperbolic with respect to suspensions of groups in 𝒢. We recover a theorem of Gautero–Lustig

    更新日期:2020-10-06
  • The KO-valued spectral flow for skew-adjoint Fredholm operators
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-09-03
    Chris Bourne; Alan L. Carey; Matthias Lesch; Adam Rennie

    In this paper, we give a comprehensive treatment of a “Clifford module flow” along paths in the skew-adjoint Fredholm operators on a real Hilbert space that takes values in KO∗(ℝ) via the Clifford index of Atiyah–Bott–Shapiro. We develop its properties for both bounded and unbounded skew-adjoint operators including an axiomatic characterization. Our constructions and approach are motivated by the principle

    更新日期:2020-09-03
  • Metric Thickenings and Group Actions
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-09-03
    Henry Adams; Mark Heim; Chris Peterson

    Let G be a group acting properly and by isometries on a metric space X; it follows that the quotient or orbit space X/G is also a metric space. We study the Vietoris–Rips and Čech complexes of X/G. Whereas (co)homology theories for metric spaces let the scale parameter of a Vietoris–Rips or Čech complex go to zero, and whereas geometric group theory requires the scale parameter to be sufficiently large

    更新日期:2020-09-03
  • A Poisson transform adapted to the Rumin complex
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-08-28
    Andreas Čap; Christoph Harrach; Pierre Julg

    Let G be a semisimple Lie group with finite center, K⊂G a maximal compact subgroup, and P⊂G a parabolic subgroup. Following ideas of P. Y. Gaillard, one may use G-invariant differential forms on G/K×G/P to construct G-equivariant Poisson transforms mapping differential forms on G/P to differential forms on G/K. Such invariant forms can be constructed using finite-dimensional representation theory.

    更新日期:2020-08-28
  • Almost flat relative vector bundles and the almost monodromy correspondence
    J. Topol. Anal. (IF 0.817) Pub Date : 2020-08-18
    Yosuke Kubota

    In this paper, we introduce the notion of almost flatness for (stably) relative bundles on a pair of topological spaces and investigate basic properties of it. First, we show that almost flatness of topological and smooth sense are equivalent. This provides a construction of an almost flat stably relative bundle on enlargeable manifolds. Second, we show the almost monodromy correspondence, that is

    更新日期:2020-08-19
  • 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
  • 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:2020-07-21
  • 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:2020-07-20
  • 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:2020-07-20
  • 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:2020-06-19
  • 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
  • There are exotic involutions on M × M
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-12-08
    Hailiang Hu

    We constructed infinitely many involutions on M×M with fixed point set homeomorphic to M. All these involutions are ℤ/2-isovariantly homotopy equivalent to interchange and are inequivalent to one another in the TOP category.

    更新日期:2019-12-08
  • Coarse quotients by group actions and the maximal Roe algebra
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-12-08
    Logan Higginbotham; Thomas Weighill

    For a finitely generated group G acting on a metric space X, Roe defined the warped space XG, which one can view as a kind of large scale quotient of X by the action of G. In this paper, we generalize this notion to the setting of actions of arbitrary groups on large scale spaces. We then restrict our attention to what we call coarsely discontinuous actions by coarse equivalences and show that for

    更新日期:2019-12-08
  • Coarse indices of twisted operators
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-12-08
    Christopher Wulff

    Several formulas for computing coarse indices of twisted Dirac type operators are introduced. One type of such formulas is by composition product in E-theory. The other type is by module multiplications in K-theory, which also yields an index theoretic interpretation of the duality between Roe algebra and stable Higson corona.

    更新日期:2019-12-08
  • The vanishing cycles of curves in toric surfaces II
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-12-08
    Rémi Crétois; Lionel Lang

    We resume the study initiated in [R. Crétois and L. Lang, The vanishing cycles of curves in toric surfaces, I, preprint (2017), arXiv:1701.00608]. For a generic curve C in an ample linear system |ℒ| on a toric surface X, a vanishing cycle of C is an isotopy class of simple closed curve that can be contracted to a point along a degeneration of C to a nodal curve in |ℒ|. The obstructions that prevent

    更新日期:2019-12-08
  • Topological 4-manifolds with right-angled Artin fundamental groups
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-12-08
    Ian Hambleton; Alyson Hildum

    We classify closed, spin+, topological 4-manifolds with fundamental group π of cohomological dimension ≤3 (up to s-cobordism), after stabilization by connected sum with at most b3(π) copies of S2×S2. In general, we must also assume that π satisfies certain K-theory and assembly map conditions. Examples for which these conditions hold include the torsion-free fundamental groups of 3-manifolds and all

    更新日期:2019-12-08
  • Quasiconformal maps on a 2-step Carnot group
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-12-08
    Christopher James Gardiner; Xiangdong Xie

    We find all global quasiconformal maps (with respect to the Carnot metric) on a particular 2-step Carnot group. In particular, all the global quasiconformal maps of this Carnot group permute the left cosets of the center, verifying a conjecture by Xie for this particular case.

    更新日期:2019-12-08
  • Geometric realizations of cyclic actions on surfaces
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-12-08
    Shiv Parsad; Kashyap Rajeevsarathy; Bidyut Sanki

    Let Mod(Sg) denote the mapping class group of the closed orientable surface Sg of genus g≥2, and let f∈Mod(Sg) be of finite order. We give an inductive procedure to construct an explicit hyperbolic structure on Sg that realizes f as an isometry. In other words, this procedure yields an explicit solution to the Nielsen realization problem for cyclic subgroups of Mod(Sg). Furthermore, we give a purely

    更新日期:2019-12-08
  • Contracting thin disks
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-12-08
    Panos Papasoglu

    We answer a question of Liokumovich–Nabutovsky–Rotman showing that if D is a Riemannian 2-disk with boundary length L, diameter d and area A≪d then D can be filled by a homotopy γt with |γt| bounded by L+2d+O(A).

    更新日期:2019-12-08
  • 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
  • Smooth crossed product of minimal unique ergodic diffeomorphisms of a manifold and cyclic cohomology
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-09-03
    Hongzhi Liu

    Different diffeomorphisms can give the same C∗ crossed product algebra. Our main purpose is to show that we can still classify dynamical systems with some appropriate smooth crossed product algebras when their corresponding C∗ crossed product algebras are isomorphic. For this purpose, we construct two minimal unique ergodic diffeomorphisms α and β of S3×S6×S8. The C∗ algebras classification theory

    更新日期:2019-09-03
  • On Vietoris–Rips complexes of ellipses
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-09-03
    Michał Adamaszek; Henry Adams; Samadwara Reddy

    For X a metric space and r>0 a scale parameter, the Vietoris–Rips simplicial complex VR<(X;r) (resp. VR≤(X;r)) has X as its vertex set, and a finite subset σ⊆X as a simplex whenever the diameter of σ is less than r (resp. at most r). Though Vietoris–Rips complexes have been studied at small choices of scale by Hausmann and Latschev [13,16], they are not well-understood at larger scale parameters. In

    更新日期:2019-09-03
  • On dimensions supporting a rational projective plane
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-09-03
    Lee Kennard; Zhixu Su

    A rational projective plane (ℚℙ2) is a simply connected, smooth, closed manifold M such that H∗(M;ℚ)≅ℚ[α]/〈α3〉. An open problem is to classify the dimensions at which such a manifold exists. The Barge–Sullivan rational surgery realization theorem provides necessary and sufficient conditions that include the Hattori–Stong integrality conditions on the Pontryagin numbers. In this paper, we simplify these

    更新日期:2019-09-03
  • Typical representatives of free homotopy classes in multi-punctured plane
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-09-03
    Maxim Arnold; Yuliy Baryshnikov; Yuriy Mileyko

    We show that a uniform probability measure supported on a specific set of piecewise linear loops in a nontrivial free homotopy class in a multi-punctured plane is overwhelmingly concentrated around loops of minimal lengths. Our approach is based on extending Mogulskii’s theorem to closed paths, which is a useful result of independent interest. In addition, we show that the above measure can be sampled

    更新日期:2019-09-03
  • Regular finite decomposition complexity
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-09-03
    Daniel Kasprowski; Andrew Nicas; David Rosenthal

    We introduce the notion of regular finite decomposition complexity of a metric family. This generalizes Gromov’s finite asymptotic dimension and is motivated by the concept of finite decomposition complexity (FDC) due to Guentner, Tessera and Yu. Regular finite decomposition complexity implies FDC and has all the permanence properties that are known for FDC, as well as a new one called Finite Quotient

    更新日期:2019-09-03
  • Non-contractible orbits for Hamiltonian functions on Riemann surfaces
    J. Topol. Anal. (IF 0.817) Pub Date : 2019-09-03
    Hiroyuki Ishiguro

    We consider two disjoint and homotopic non-contractible embedded loops on a Riemann surface and prove the existence of a non-contractible orbit for a Hamiltonian function on the surface whenever it is sufficiently large on one of the loops and sufficiently small on the other. This gives the first example of an estimate from above for a generalized form of the Biran–Polterovich–Salamon capacity for

    更新日期:2019-09-03
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