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∗-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 s...
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Walter de Gruyter GmbH
2015
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| LEADER | 04199caa a22004457a 4500 | ||
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| 001 | PAPER-13946 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518204423.0 | ||
| 008 | 190411s2015 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-84990216590 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Cortiñas, G. | |
| 245 | 1 | 0 | |a Compact operators and algebraic K-theory for groups which act properly and isometrically on Hilbert space |
| 260 | |b Walter de Gruyter GmbH |c 2015 | ||
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Bartels, A., Lück, W., Isomorphism conjecture for homotopy K-theory and groups acting on trees (2006) J. Pure Appl. Algebra, 205, pp. 660-696 | ||
| 504 | |a Cortiñas, G., Ellis, E., Isomorphism conjectures with proper coefficients (2014) J. Pure Appl. Algebra, 218, pp. 1224-1263 | ||
| 504 | |a Cuntz, J., Meyer, R., Rosenberg, J.M., Topological and bivariant K-theory (2007) Oberwolfach Semin., 36. , Birkhäuser, Basel | ||
| 504 | |a Davis, J.F., Lück, W., Spaces over a category and assembly maps in isomorphism conjectures in K- and L-theory (1998) K-Theory, 15, pp. 201-252 | ||
| 504 | |a Gromov, M., (1993) Geometric Group Theory. Vol. 2: Asymptotic Invariants of Infinite Groups, , London Math. Soc. Lecture Note Ser. 182, Cambridge University Press, Cambridge | ||
| 504 | |a Guentner, E., Higson, N., Trout, J., Equivariant E-theory for C∗-algebras (2000) Mem. Amer. Math. Soc., 148 (703) | ||
| 504 | |a Hambleton, I., Pedersen, E.K., Identifying assembly maps in K- and L-theory (2004) Math. Ann., 328, pp. 27-57 | ||
| 504 | |a Higson, N., Algebraic K-theory of stable C∗-algebras (1988) Adv. Math., 67 (1) | ||
| 504 | |a Higson, N., Kasparov, G., Operator K-theory for groups which act properly and isometrically on hilbert space (1997) Electron. Res. Announc. Amer. Math. Soc., 3, pp. 131-142 | ||
| 504 | |a Higson, N., Kasparov, G., E-theory and KK-theory for groups which act properly and isometrically on hilbert space (2001) Invent. Math., 144, pp. 23-74 | ||
| 504 | |a Higson, N., Kasparov, G., Trout, J., A bott periodicity theorem for infinite dimensional euclidean space (1998) Adv. Math., 135, pp. 1-40 | ||
| 504 | |a Rosenberg, J., Comparison between algebraic and topological K-theory for banach algebras and C∗-algebras (2005) Handbook of K-theory, 1-2, pp. 843-874. , Springer, Berlin | ||
| 504 | |a Suslin, A.A., Wodzicki, M., Excision in algebraic K-theory (1992) Ann. of Math., 136, pp. 51-122. , (2) | ||
| 504 | |a Wegge-Olsen, N.E., (1993) K-theory and C∗-algebras, , Oxford University Press, New York | ||
| 504 | |a Weibel, C.A., Homotopy algebraic K-theory (1989) Algebraic K-theory and Algebraic Number Theory (Honolulu 1987), pp. 461-488. , Contemp. Math. 83 American Mathematical Society, Providence | ||
| 520 | 3 | |a We prove the K-theoretic Farrell-Jones conjecture for groups with the Haagerup approximation property and coefficient rings and 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∗-crossed product of G with a stable separable G-C∗-algebra have the same K-theory. © 2015 De Gruyter. |l eng | |
| 593 | |a Departamento de Matemática-IMAS, FCEyN-UBA, Ciudad Universitaria Pab 1, Buenos Aires, 1428, Argentina | ||
| 700 | 1 | |a Tartaglia, G. | |
| 773 | 0 | |d Walter de Gruyter GmbH, 2015 |g v. 2015 |p J. Reine Angew. Math. |x 00754102 |w (AR-BaUEN)CENRE-1036 |t Journal fur die Reine und Angewandte Mathematik | |
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| 856 | 4 | 0 | |u https://doi.org/10.1515/crelle-2014-0154 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00754102_v2015_n_p_Cortinas |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00754102_v2015_n_p_Cortinas |y Registro en la Biblioteca Digital |
| 961 | |a paper_00754102_v2015_n_p_Cortinas |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||