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.
"A homological characterization of topological amenability." Algebr. Geom. Topol. 12 (3) 1763 - 1776, 2012. https://doi.org/10.2140/agt.2012.12.1763