A homology theory for étale groupoids

Abstract

Etale groupoids arise naturally as models for leaf spaces of foliations for orbifolds and for orbit spaces of discrete group actions In this paper we introduce a sheaf homology theory for etale groupoids We prove its invariance under Morita equivalence as well as Verdier duality between Haeiger cohomology and this homology We also discuss the relation to the cyclic and Hochschild homologies of Connes convolution algebra of the groupoid and derive some spectral sequences which serve as a tool for the computation of these homologies