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A
homological characterization of topological amenability
Jacek Brodzki, Graham A Niblo, Piotr W Nowak and Nick Wright |
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Algebraic & Geometric Topology 12 (2012) 1763–1776
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Abstract |
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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 on its Stone–Čech compactification we obtain a homological characterization of exactness of the group. |
Keywords
topological amenability, uniformly finite homology, exact
groups
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Mathematical Subject Classification 2000
Primary: 43A07
Secondary: 37A15, 58E40, 46L55
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References |
Publication
Received: 14 July 2011
Revised: 20 April 2012
Accepted: 7 May 2012
Published: 8 August 2012
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Authors |
| Jacek Brodzki | |
| School of Mathematics University of Southampton Highfield Southampton SO17 1SH United Kingdom |
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| Graham A Niblo | |
| School of Mathematics University of Southampton Highfield Southampton SO17 1SH United Kingdom |
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| 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 |
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