Algebraic & Geometric Topology

A homological characterization of topological amenability

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

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

topological amenability uniformly finite homology exact groups


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.

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