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A homology theory for étale groupoids

✍ Scribed by Crainic, Marius; Moerdijk, Ieke

Book ID
111981245
Publisher
Walter de Gruyter GmbH & Co. KG
Year
2000
Tongue
English
Weight
211 KB
Volume
2000
Category
Article
ISSN
0075-4102

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✦ Synopsis

E Â tale 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 e Âtale groupoids. We prove its invariance under Morita equivalence, as well as Verdier duality between Hae¯iger 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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