A Homology Theory for Etale Groupoids, by Marius Crainic and Ieke Moerdijk

In this paper we introduce a homology theory for etale groupoids, dual to Haefliger's cohomology theory (via Poincare duality). We prove basic facts like Morita invariance, Leray spectral sequence, Verdier duality. We also outline the application to the computation of cyclic homology of the convolution algebra of the groupoid (including the non-Hausdorff situation). An appendix about "compact supports" on non-Hausdorff manifolds is added.

Marius Crainic <crainic@math.ruu.nl>
Ieke Moerdijk <moerdijk@math.ruu.nl>