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K-theory for subspaces of groups

K-theory for subspaces of groups
K-theory for subspaces of groups
We show that a subspace of a group carries a natural partial translation structure which gives rise to a C*-algebra similar to that of a reduced C*-algebra of a group. We investigate the question: Does the inclusion of a subspace into an ambient group induce a homomorphism of C*-algebras? We prove that the answer is affirmative for subspaces of groups with non-coarsely dense complement. We show that under this condition there exists an exact sequence of C*-algebras which is analogous to the Pimsner-Voiculescu extension.
Brodzki, J
b1fe25fd-5451-4fd0-b24b-c59b75710543
Niblo, G.A
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Putwain, R.J
ad2d0d86-3dca-4dfc-b7bf-5cd5c59a3f18
Wright, N.J
f4685b8d-7496-47dc-95f0-aba3f70fbccd
Brodzki, J
b1fe25fd-5451-4fd0-b24b-c59b75710543
Niblo, G.A
43fe9561-c483-4cdf-bee5-0de388b78944
Putwain, R.J
ad2d0d86-3dca-4dfc-b7bf-5cd5c59a3f18
Wright, N.J
f4685b8d-7496-47dc-95f0-aba3f70fbccd

Brodzki, J, Niblo, G.A, Putwain, R.J and Wright, N.J (2010) K-theory for subspaces of groups. Pre-print.

Record type: Article

Abstract

We show that a subspace of a group carries a natural partial translation structure which gives rise to a C*-algebra similar to that of a reduced C*-algebra of a group. We investigate the question: Does the inclusion of a subspace into an ambient group induce a homomorphism of C*-algebras? We prove that the answer is affirmative for subspaces of groups with non-coarsely dense complement. We show that under this condition there exists an exact sequence of C*-algebras which is analogous to the Pimsner-Voiculescu extension.

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Published date: 2010
Additional Information: In review

Identifiers

Local EPrints ID: 149575
URI: https://eprints.soton.ac.uk/id/eprint/149575
PURE UUID: 22393331-30e5-4e8e-ab00-2dfeae67dfd7
ORCID for G.A Niblo: ORCID iD orcid.org/0000-0003-0648-7027
ORCID for N.J Wright: ORCID iD orcid.org/0000-0003-4884-2576

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Date deposited: 10 May 2010 08:37
Last modified: 13 Jun 2019 00:39

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