A homological characterization of topological amenability

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.