Geodesic
A homological characterization of topological amenability
Brodzki, Jacek1 ; Niblo, Graham1 ; Nowak, Piotr2 ; Wright, Nick1
1School of Mathematics, University of Southampton, Highfield, Southampton, SO17 1SH, United Kingdom
2Faculty 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
Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1763-1776
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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.

DOI : 10.2140/agt.2012.12.1763
Keywords: topological amenability, uniformly finite homology, exact groups

Brodzki, Jacek  1   ; Niblo, Graham  1   ; Nowak, Piotr  2   ; Wright, Nick  1

1 School of Mathematics, University of Southampton, Highfield, Southampton, SO17 1SH, United Kingdom
2 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 
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Brodzki, Jacek; Niblo, Graham; Nowak, Piotr; Wright, Nick. A homological characterization of topological amenability. Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1763-1776. doi: 10.2140/agt.2012.12.1763

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