Geodesic
Non-Hausdorff groupoids, proper actions and $K$-theory
Documenta mathematica, Tome 9 (2004), pp. 565-597
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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 Cr∗​(G2​) to Cr∗​(G1​), and thus two Morita equivalent groupoids have Morita-equivalent C∗-algebras.
DOI : 10.4171/dm/178
Classification : 22A22, 46L05, 46L80, 54D35
Mots-clés : groupoid, C∗-algebra, K-theory 
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     author = {Jean-Louis Tu},
     title = {Non-Hausdorff groupoids, proper actions and $K$-theory},
     journal = {Documenta mathematica},
     pages = {565--597},
     year = {2004},
     volume = {9},
     doi = {10.4171/dm/178},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/178/}
}
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Jean-Louis Tu. Non-Hausdorff groupoids, proper actions and $K$-theory. Documenta mathematica, Tome 9 (2004), pp. 565-597. doi: 10.4171/dm/178

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