Algebraic & Geometric Topology

A homological characterization of topological amenability

Jacek Brodzki, Graham Niblo, Piotr Nowak, and Nick Wright

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Abstract

Generalizing Block and Weinberger’s characterization of amenability we introduce the notion of uniformly finite homology for a group action on a compact space and use it to give a homological characterization of topological amenability for actions. By considering the case of the natural action of G on its Stone–Čech compactification we obtain a homological characterization of exactness of the group.

Article information

Source
Algebr. Geom. Topol., Volume 12, Number 3 (2012), 1763-1776.

Dates
Received: 14 July 2011
Revised: 20 April 2012
Accepted: 7 May 2012
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715415

Digital Object Identifier
doi:10.2140/agt.2012.12.1763

Mathematical Reviews number (MathSciNet)
MR2966703

Zentralblatt MATH identifier
1251.43001

Subjects
Primary: 43A07: Means on groups, semigroups, etc.; amenable groups
Secondary: 37A15: General groups of measure-preserving transformations [See mainly 22Fxx] 58E40: Group actions 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]

Keywords
topological amenability uniformly finite homology exact groups

Citation

Brodzki, Jacek; Niblo, Graham; Nowak, Piotr; Wright, Nick. A homological characterization of topological amenability. Algebr. Geom. Topol. 12 (2012), no. 3, 1763--1776. doi:10.2140/agt.2012.12.1763. https://projecteuclid.org/euclid.agt/1513715415


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