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Two remarks about the Baum-Connes map. (Deux remarques sur l’application de Baum-Connes.) (French) Zbl 1003.46037
Summary: Let $$G$$ be a locally compact Hausdorff group. The authors show in first part that a space endowed with a proper action of $$G$$ is locally induced from spaces with an action of a compact subgroup of $$G$$. As a consequence for the Baum-Connes map, the slice condition can be removed from the notion of proper action in the definition of the topological theory of a group. In a second part, they show that the Baum-Connes map for $$G$$ with coefficients in a proper algebra is an isomorphism.

MSC:
 46L55 Noncommutative dynamical systems 46L80 $$K$$-theory and operator algebras (including cyclic theory)
Keywords:
Baum-Connes map; slice condition
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