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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
A homological characterization of topological amenability

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

Algebraic & Geometric Topology 12 (2012) 1763–1776
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.

Keywords
topological amenability, uniformly finite homology, exact groups
Mathematical Subject Classification 2000
Primary: 43A07
Secondary: 37A15, 58E40, 46L55
References
Publication
Received: 14 July 2011
Revised: 20 April 2012
Accepted: 7 May 2012
Published: 8 August 2012
Authors
Jacek Brodzki
School of Mathematics
University of Southampton
Highfield
Southampton
SO17 1SH
United Kingdom
Graham A Niblo
School of Mathematics
University of Southampton
Highfield
Southampton
SO17 1SH
United Kingdom
Piotr W Nowak
Faculty of Mathematics, Informatics and Mechanics
University of Warsaw
Banacha 2
02-097 Warsaw
Poland
Institute of Mathematics of the Polish Academy of Sciences
Śniadeckich 8
00-956 Warsaw
Poland
Nick Wright
School of Mathematics
University of Southampton
Highfield
Southampton
SO17 1SH
United Kingdom