Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space
We prove the K-theoretic Farrell-Jones conjecture for groups with the Haagerup approximation property and coefficient rings and C ∗ C^{∗} -algebras which are stable with respect to compact operators. We use this and Higson-Kasparov's result that the Baum-Connes conjecture holds for such a group...
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| Autores principales: | , |
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| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00754102_v2018_n734_p265_Cortinas |
| Aporte de: |
| Sumario: | We prove the K-theoretic Farrell-Jones conjecture for groups with the Haagerup approximation property and coefficient rings and C ∗ C^{∗} -algebras which are stable with respect to compact operators. We use this and Higson-Kasparov's result that the Baum-Connes conjecture holds for such a group G, to show that the algebraic and the C ∗ C^{∗} -crossed product of G with a stable separable G- C ∗ C^{∗} -algebra have the same K-theory. © 2018 Walter de Gruyter GmbH, Berlin/Boston. |
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