Non-Hausdorff groupoids, proper actions and -theory
Jean-Louis Tu
University Paris VI Institut de Mathématiques 175, rue du Chevaleret 75013 Paris, France
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Abstract
Let be a (not necessarily Hausdorff) locally compact groupoid. We introduce a notion of properness for , which is invariant under Morita-equivalence. We show that any generalized morphism between two locally compact groupoids which satisfies some properness conditions induces a -correspondence from to , and thus two Morita equivalent groupoids have Morita-equivalent -algebras.
Cite this article
Jean-Louis Tu, Non-Hausdorff groupoids, proper actions and -theory. Doc. Math. 9 (2004), pp. 565–597
DOI 10.4171/DM/178