Abstract:
Let G be a group and let KH be homotopy algebraic K-theory. We prove that if G satisfies the rational KH isomorphism conjecture for the group algebra L1[G] with coefficients in the algebra of trace-class operators in Hilbert space, then it also satisfies the Ktheoretic Novikov conjecture for the group algebra over the integers, and the rational injectivity part of the Farrell-Jones conjecture with coefficients in any number field.
Registro:
Documento: |
Artículo
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Título: | Trace class operators, regulators, and assembly maps in K-theory |
Autor: | Cortiñas, G.; Tartaglia, G. |
Filiación: | Dep. de Matemática-IMAS, F. Cs. Exactas y Naturales, University de Buenos Aires, Ciudad Universitaria Pab 1, 1428 Buenos Aires, Argentina
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Palabras clave: | Borel regulator; Homotopy algebraic k-theory; Multiplicative k-theory; Trace-class operators |
Año: | 2014
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Volumen: | 19
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Número: | 1
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Página de inicio: | 439
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Página de fin: | 455
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Título revista: | Documenta Mathematica
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Título revista abreviado: | Doc. Math.
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ISSN: | 14310635
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14310635_v19_n1_p439_Cortinas |
Referencias:
- Bartels, A., Lück, W., Isomorphism conjecture for homotopy K-theory and groups acting on trees (2006) J. Pure Appl. Algebra, 205 (3), pp. 660-696
- Cortiñas, G., Algebraic v. topological K-theory: a friendly match, Topics in algebraic and topological K-theory (2011) Lecture Notes in Math, 2008, pp. 103-165. , Springer Berlin
- Cortiñas, G., Ellis, E., Isomorphism conjectures with proper coefficients (2014) J. Pure Appl. Algebra, 218, pp. 1224-1263. , DOI10.1016/j.jpaa.2013.11.016
- Cortiñas, G., Tartaglia, G., Operator ideals and assembly maps in K-theory (2014) Proc. Amer. Math. Soc., 142, pp. 1089-1099
- Cortiñas, G., Thom, A., Comparison between algebraic and topological K-theory of locally convex algebras (2008) Adv. Math., 218 (1), pp. 266-307
- Cuntz, J., Quillen, D., Excision in bivariant periodic cyclic cohomology (1997) Invent. Math., 127 (1), pp. 67-98
- Karoubi, M., Homologie cyclique et K-théorie (1987) Astérisque, 149 (147). , French, with English summary
- Karoubi, M., Sur la K-théorie multiplicative, Cyclic cohomology and noncommutative geometry (Waterloo, ON, 1995) (1997) Fields Inst. Commun., 17, pp. 59-77. , Amer. Math. Soc., Providence, RI (French, with English summary)
- Lück, W., Chern characters for proper equivariant homology theories and applications to K- and L-theory (2002) J. Reine Angew. Math., 543, pp. 193-234
- Lück, W., The relation between the Baum-Connes conjecture and the trace conjecture (2002) Invent. Math., 149 (1), pp. 123-152
- Lück, W., Reich, H., The Baum-Connes and the Farrell-Jones conjectures in K- and L-theory (2005) Handbook of K-theory, 1 (2), pp. 703-842. , Springer Berlin
- Lück, W., Reich, H., Detecting K-theory by cyclic homology (2006) Proc. London Math. Soc., 3 (93), pp. 593-634. , no. 3
- Weibel, C.A., Homotopy algebraic K-theory, Algebraic K-theory and algebraic number theory (Honolulu, HI, 1987) (1989) Contemp. Math., 83, pp. 461-488. , Amer. Math. Soc., Providence, RI
- Yu, G., The algebraic K-theory Novikov conjecture for group algebras over the ring of Schatten class operators arXiv:1106.3796
Citas:
---------- APA ----------
Cortiñas, G. & Tartaglia, G.
(2014)
. Trace class operators, regulators, and assembly maps in K-theory. Documenta Mathematica, 19(1), 439-455.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14310635_v19_n1_p439_Cortinas [ ]
---------- CHICAGO ----------
Cortiñas, G., Tartaglia, G.
"Trace class operators, regulators, and assembly maps in K-theory"
. Documenta Mathematica 19, no. 1
(2014) : 439-455.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14310635_v19_n1_p439_Cortinas [ ]
---------- MLA ----------
Cortiñas, G., Tartaglia, G.
"Trace class operators, regulators, and assembly maps in K-theory"
. Documenta Mathematica, vol. 19, no. 1, 2014, pp. 439-455.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14310635_v19_n1_p439_Cortinas [ ]
---------- VANCOUVER ----------
Cortiñas, G., Tartaglia, G. Trace class operators, regulators, and assembly maps in K-theory. Doc. Math. 2014;19(1):439-455.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14310635_v19_n1_p439_Cortinas [ ]