ar X iv : m at h / 99 05 01 1 v 1 [ m at h . K T ] 3 M ay 1 99 9 A Homology Theory for Étale Groupoids ∗
نویسندگان
چکیده
Étale 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 forétale groupoids. We prove its invariance under Morita equivalence, as well as Verdier duality between Haefliger 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.
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