Equivariant K-Homology and Restriction to Finite Cyclic Subgroups |
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Authors: | Michel Matthey and Guido Mislin |
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Affiliation: | (1) University of lausanne, IGAT, BCH, EPFL, CH-1015 Lausanne, Switzerland;(2) Department of Mathematics, ETH Zentrum, CH-8092 Zürich, Switzerland |
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Abstract: | For a discrete group G, we prove that a G-map between proper G–CW-complexes induces an isomorphism in G-equivariant K-homology if it induces an isomorphism in C-equivariant K-homology for every finite cyclic subgroup C of G. As an application, we show that the source of the Baum–Connes assembly map, namely K*G (E(G, in)), is isomorphic to K*G (E(G, )), where E(G, ) denotes the classifying space for the family of finite cyclic subgroups of G. Letting be the family of virtually cyclic subgroups of G, we also establish that and related results. |
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Keywords: | Boom-Connes Conjectune equivariant homology theries families of subgroups K-homology |
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