Authors:D. Alvarez-Gavela, V. Kaminker, A. Kislev, K. Kliakhandler, A. Pavlichenko, L. Rigolli, D. Rosen, O. Shabtai, B. Stevenson, J. Zhang Pages: 1 - 32 Abstract: Journal of Topology and Analysis, Ahead of Print. Given a symplectic surface [math] of genus [math], we show that the free group with two generators embeds into every asymptotic cone of [math], where [math] is the Hofer metric. The result stabilizes to products with symplectically aspherical manifolds. Citation: Journal of Topology and Analysis PubDate: 2018-05-18T08:54:14Z DOI: 10.1142/S1793525319500213
Authors:Ian Hambleton, Alyson Hildum Pages: 1 - 45 Abstract: Journal of Topology and Analysis, Ahead of Print. We classify closed, [math], topological [math]-manifolds with fundamental group [math] of cohomological dimension [math] (up to [math]-cobordism), after stabilization by connected sum with at most [math] copies of [math]. In general, we must also assume that [math] satisfies certain [math]-theory and assembly map conditions. Examples for which these conditions hold include the torsion-free fundamental groups of [math]-manifolds and all right-angled Artin groups whose defining graphs have no [math]-cliques. Citation: Journal of Topology and Analysis PubDate: 2018-04-23T08:56:28Z DOI: 10.1142/S1793525319500328
Authors:Christopher James Gardiner, Xiangdong Xie Pages: 1 - 24 Abstract: Journal of Topology and Analysis, Ahead of Print. We find all global quasiconformal maps (with respect to the Carnot metric) on a particular [math]-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. Citation: Journal of Topology and Analysis PubDate: 2018-04-12T02:20:53Z DOI: 10.1142/S1793525319500316
Authors:David Constantine, Jean-François Lafont Pages: 1 - 37 Abstract: Journal of Topology and Analysis, Ahead of Print. In a compact geodesic metric space of topological dimension one, the minimal length of a loop in a free homotopy class is well-defined, and provides a function [math] (the value [math] being assigned to loops which are not freely homotopic to any rectifiable loops). This function is the marked length spectrum. We introduce a subset [math], which is the union of all non-constant minimal loops of finite length. We show that if [math] is a compact, non-contractible, geodesic space of topological dimension one, then [math] deformation retracts to [math]. Moreover, [math] can be characterized as the minimal subset of [math] to which [math] deformation retracts. Let [math] be a pair of compact, non-contractible, geodesic metric spaces of topological dimension one, and set [math]. We prove that any isomorphism [math] satisfying [math], forces the existence of an isometry [math] which induces the map [math] on the level of fundamental groups. Thus, for compact, non-contractible, geodesic spaces of topological dimension one, the marked length spectrum completely determines the subset [math] up to isometry. Citation: Journal of Topology and Analysis PubDate: 2018-02-21T04:11:29Z DOI: 10.1142/S1793525319500250
Authors:Hongzhi Liu Pages: 1 - 13 Abstract: Journal of Topology and Analysis, Ahead of Print. Different diffeomorphisms can give the same [math] 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 [math] crossed product algebras are isomorphic. For this purpose, we construct two minimal unique ergodic diffeomorphisms [math] and [math] of [math]. The [math] algebras classification theory, smooth crossed product algebras considered by R. Nest and cyclic cohomology are used to show that [math] and [math] give the same [math] algebra and induce different smooth crossed product algebras. Citation: Journal of Topology and Analysis PubDate: 2018-01-31T06:37:58Z DOI: 10.1142/S1793525319500304
Authors:Stéphane Sabourau, Zeina Yassine Pages: 1 - 18 Abstract: Journal of Topology and Analysis, Ahead of Print. It is known that the genus two surface admits a piecewise flat metric with conical singularities which is extremal for the systolic inequality among all nonpositively curved metrics. We prove that this piecewise flat metric is also critical for slow metric variations, without curvature restrictions, for another type of systolic inequality involving the lengths of the shortest noncontractible loops in different free homotopy classes. The free homotopy classes considered correspond to those of the systolic loops and the second systolic loops of the extremal surface. Citation: Journal of Topology and Analysis PubDate: 2018-01-30T08:53:42Z DOI: 10.1142/S1793525319500298
Authors:Daniel Kasprowski, Andrew Nicas, David Rosenthal Pages: 1 - 29 Abstract: Journal of Topology and Analysis, Ahead of Print. 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 Permanence. We show that for a collection containing all metric families with finite asymptotic dimension, all other permanence properties follow from Fibering Permanence. Citation: Journal of Topology and Analysis PubDate: 2018-01-25T03:02:42Z DOI: 10.1142/S1793525319500286
Authors:Michał Adamaszek, Henry Adams, Samadwara Reddy Pages: 1 - 30 Abstract: Journal of Topology and Analysis, Ahead of Print. For [math] a metric space and [math] a scale parameter, the Vietoris–Rips simplicial complex [math] (resp. [math]) has [math] as its vertex set, and a finite subset [math] as a simplex whenever the diameter of [math] is less than [math] (resp. at most [math]). 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 this paper we investigate the homotopy types of Vietoris–Rips complexes of ellipses [math] of small eccentricity, meaning [math]. Indeed, we show that there are constants [math] such that for all [math], we have [math] and [math], though only one of the two-spheres in [math] is persistent. Furthermore, we show that for any scale parameter [math], there are arbitrarily dense subsets of the ellipse such that the Vietoris–Rips complex of the subset is not homotopy equivalent to the Vietoris–Rips complex of the entire ellipse. As our main tool we link these homotopy types to the structure of infinite cyclic graphs. Citation: Journal of Topology and Analysis PubDate: 2018-01-03T07:15:48Z DOI: 10.1142/S1793525319500274
Hybrid journal (It can contain Open Access articles)
[119 journals]
