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Non-Hausdorff groupoids, proper actions and K-theory

Jean-Louis Tu
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Abstract

Let G be a (not necessarily Hausdorff) locally compact groupoid. We introduce a notion of properness for G, which is invariant under Morita-equivalence. We show that any generalized morphism between two locally compact groupoids which satisfies some properness conditions induces a C*-correspondence from $C*_r(G_1)$ to $C^*_r(G_2)$, and thus two Morita equivalent groupoids have Morita-equivalent $C^*$-algebras.

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Jean-Louis Tu. 2004-09-13. Non-Hausdorff groupoids, proper actions and K-theory. https://arxiv.org/abs/math/0403071

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