A Homology Theory for Etale Groupoids
K-Theory and Homology
2007-05-23 v1 Algebraic Topology
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 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.
Cite
@article{arxiv.math/9905011,
title = {A Homology Theory for Etale Groupoids},
author = {Marius Crainic and Ieke Moerdijk},
journal= {arXiv preprint arXiv:math/9905011},
year = {2007}
}
Comments
34 pages