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On the K-theory of groups with finite decomposition complexity

On the K-theory of groups with finite decomposition complexity
On the K-theory of groups with finite decomposition complexity
It is proved that the assembly map in algebraic K- and L-theory with respect to the family of finite subgroups is injective for groups Γ with finite quotient finite decomposition complexity (a strengthening of finite decomposition complexity introduced by Guentner, Tessera and Yu) that admit a finite-dimensional model for EΓ and have an upper bound on the order of their finite subgroups. In particular, this applies to finitely generated linear groups over fields with characteristic zero with a finite-dimensional model for EΓ.
0024-6115
565-592
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075

Kasprowski, Daniel (2015) On the K-theory of groups with finite decomposition complexity. Proceedings of the London Mathematical Society, 110 (3), 565-592. (doi:10.1112/plms/pdu062).

Record type: Article

Abstract

It is proved that the assembly map in algebraic K- and L-theory with respect to the family of finite subgroups is injective for groups Γ with finite quotient finite decomposition complexity (a strengthening of finite decomposition complexity introduced by Guentner, Tessera and Yu) that admit a finite-dimensional model for EΓ and have an upper bound on the order of their finite subgroups. In particular, this applies to finitely generated linear groups over fields with characteristic zero with a finite-dimensional model for EΓ.

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Published date: 6 December 2015
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Local EPrints ID: 478531
URI: http://eprints.soton.ac.uk/id/eprint/478531
DOI: doi:10.1112/plms/pdu062
ISSN: 0024-6115
PURE UUID: e81c9525-0f8f-40df-843c-263a90c7bcbc
ORCID for Daniel Kasprowski: ORCID iD orcid.org/0000-0001-5926-2206

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Date deposited: 04 Jul 2023 17:48
Last modified: 17 Mar 2024 04:19

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Author: Daniel Kasprowski ORCID iD

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