Complexes and exactness of certain Artin groups
Complexes and exactness of certain Artin groups
In his work on the Novikov conjecture, Yu introduced Property A as a readily verified criterion implying coarse embeddability. Studied subsequently as a property in its own right, Property A for a discrete group is known to be equivalent to C*-exactness of the reduced C*-algebra, and to the amenability of the action of the group on its Stone-Cech compactification. In this paper we study exactness for groups acting on a finite dimensional CAT(0) cube complex. We apply our methods to show that Artin groups of type FC are exact. While many discrete groups are known to be exact the question of whether every Artin group is exact remains open.
1471-1495
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Guentner, Erik
0efa2b74-da7d-497d-8a80-e668eb8f41f1
23 May 2011
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Guentner, Erik
0efa2b74-da7d-497d-8a80-e668eb8f41f1
Niblo, Graham A. and Guentner, Erik
(2011)
Complexes and exactness of certain Artin groups.
Algebraic & Geometric Topology, 11 (3), Summer Issue, .
(doi:10.2140/agt.2011.11.1471).
Abstract
In his work on the Novikov conjecture, Yu introduced Property A as a readily verified criterion implying coarse embeddability. Studied subsequently as a property in its own right, Property A for a discrete group is known to be equivalent to C*-exactness of the reduced C*-algebra, and to the amenability of the action of the group on its Stone-Cech compactification. In this paper we study exactness for groups acting on a finite dimensional CAT(0) cube complex. We apply our methods to show that Artin groups of type FC are exact. While many discrete groups are known to be exact the question of whether every Artin group is exact remains open.
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Accepted/In Press date: 24 January 2011
Published date: 23 May 2011
Organisations:
Mathematical Sciences, Pure Mathematics
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Local EPrints ID: 159253
URI: http://eprints.soton.ac.uk/id/eprint/159253
ISSN: 1472-2747
PURE UUID: 3fd14a82-f740-4b50-bb38-3a645caf5419
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Date deposited: 29 Jun 2010 15:33
Last modified: 14 Mar 2024 02:36
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Author:
Erik Guentner
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