On exactness and isoperimetric profiles of discrete groups
type: Item
instance of: scholarly article
title: On exactness and isoperimetric profiles of discrete groups
zbMATH Open document ID: 1117.60008
author: Piotr W. Nowak
published in: Journal of Functional Analysis
publication date: 2007-02-26T00:00:00Z
review text: From author's abstract: We introduce a quasi-isometry invariant related to Property A and explore its connections to various other invariants of finitely generated groups. This allows to establish a direct relation between the asymptotic dimension on one hand and random walks on the other. Property A has been introduced by \textit{G. Yu} in [Invent. Math. 139, No.~1, 201--240 (2000; Zbl 0956.19004)]. The present paper is also related to Vershik's works on amenable groups.
Mathematics Subject Classification ID: 60B15
zbMATH DE Number: 5129777
zbMATH Keywords: amenability
zbMATH Keywords: property A
zbMATH Keywords: isoperimetric profile
zbMATH Keywords: coarse embedding
reviewed by: Yasuhiro Asoo
MaRDI profile type: Publication
full work available at URL: j.jfa.2006.10.011
OpenAlex ID: W2003942393
cites work: Metrics on diagram groups and uniform embeddings in a Hilbert space.
cites work: Q3938871
cites work: Q3502037
cites work: Property A for groups acting on metric spaces.
cites work: On asymptotic dimension of groups
cites work: A Hurewicz-type theorem for asymptotic dimension and applications to geometric group theory
cites work: Compression of uniform embeddings into Hilbert space.
cites work: A Hurewicz theorem for the Assouad-Nagata dimension
cites work: Embedding of hyperbolic spaces in the product of trees
cites work: Hyperbolic dimension of metric spaces
cites work: Hilbert space compression and exactness of discrete groups.
cites work: Uniform embeddability and exactness of free products.
cites work: Distortion of wreath products in some finitely presented groups.
cites work: Isoperimetricity for groups and manifolds
cites work: Q3607418
cites work: Constructions preserving Hilbert space uniform embeddability of discrete groups
cites work: Every Coxeter group acts amenably on a compact space
cites work: Asymptotic dimension of discrete groups
cites work: Universal spaces for asymptotic dimension
cites work: On isoperimetric profiles of finitely generated groups.
cites work: A rigidity theorem for the solvable Baumslag-Solitar groups. (With an appendix by Daryl Cooper)
cites work: Asymptotic dimension of finitely presented groups
cites work: Q5562332
cites work: The lamplighter group as a group generated by a 2-state automaton, and its spectrum
cites work: Random walk in random groups.
cites work: Exactness of one relator groups
cites work: Exactness and the Novikov conjecture
cites work: EXACTNESS AND UNIFORM EMBEDDABILITY OF DISCRETE GROUPS
cites work: The Novikov conjecture for linear groups
cites work: Amenable group actions and the Novikov conjecture
cites work: Filling invariants of systolic complexes and groups.
cites work: Random walks on discrete groups: Boundary and entropy
cites work: Q3378996
cites work: On coarse embeddability into lp-spaces and a conjecture of Dranishnikov
cites work: Coarsely embeddable metric spaces without Property A
cites work: Amenable actions and exactness for discrete groups
cites work: Q3756753
cites work: Q4263828
cites work: Random walks on finite rank solvable groups.
cites work: Q4437801
cites work: Hyperbolic groups have finite asymptotic dimension
cites work: Probability on groups: Random walks and invariant diffusions
cites work: Q3160540
cites work: Remarks on Yu's `property {A}' for discrete metric spaces and groups.
cites work: Q5665644
cites work: The Novikov conjecture for groups with finite asymptotic dimension
cites work: The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
DOI: 10.1016/J.JFA.2006.10.011
description: scientific article; zbMATH DE number 5129777