A Homology Theory for Etale Groupoids

Details A Homology Theory for Etale Groupoids A Homology Theory for Etale Groupoids

1999-05-03

arxiv.org/abs/math/9905011v1

Mathematics

K-Theory and Homology

34 pages

Scientific paper

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 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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