A homological characterization of topological amenability

Details A homological characterization of topological amenability A homological characterization of topological amenability

2010-08-24

arxiv.org/abs/1008.4154v2

Mathematics

Group Theory

Updated to include a discussion of functoriality

Scientific paper

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-\vCech compactification we obtain a homological characterization of exactness of the group, answering a question of Nigel Higson.

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