Trace class operators, regulators, and assembly maps in K-theory

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 gro...

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Detalles Bibliográficos
Autores principales: Cortiñas, G., Tartaglia, G.
Formato: JOUR
Materias:
Borel regulator
Homotopy algebraic k-theory
Multiplicative k-theory
Trace-class operators
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_14310635_v19_n1_p439_Cortinas
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_14310635_v19_n1_p439_Cortinas
record_format dspace
spelling todo:paper_14310635_v19_n1_p439_Cortinas2023-10-03T16:13:51Z Trace class operators, regulators, and assembly maps in K-theory Cortiñas, G. Tartaglia, G. Borel regulator Homotopy algebraic k-theory Multiplicative k-theory Trace-class operators 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_14310635_v19_n1_p439_Cortinas
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Borel regulator
Homotopy algebraic k-theory
Multiplicative k-theory
Trace-class operators
spellingShingle Borel regulator
Homotopy algebraic k-theory
Multiplicative k-theory
Trace-class operators
Cortiñas, G.
Tartaglia, G.
Trace class operators, regulators, and assembly maps in K-theory
topic_facet Borel regulator
Homotopy algebraic k-theory
Multiplicative k-theory
Trace-class operators
description 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.
format JOUR
author Cortiñas, G.
Tartaglia, G.
author_facet Cortiñas, G.
Tartaglia, G.
author_sort Cortiñas, G.
title Trace class operators, regulators, and assembly maps in K-theory
title_short Trace class operators, regulators, and assembly maps in K-theory
title_full Trace class operators, regulators, and assembly maps in K-theory
title_fullStr Trace class operators, regulators, and assembly maps in K-theory
title_full_unstemmed Trace class operators, regulators, and assembly maps in K-theory
title_sort trace class operators, regulators, and assembly maps in k-theory
url http://hdl.handle.net/20.500.12110/paper_14310635_v19_n1_p439_Cortinas
work_keys_str_mv AT cortinasg traceclassoperatorsregulatorsandassemblymapsinktheory
AT tartagliag traceclassoperatorsregulatorsandassemblymapsinktheory
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