Property A, partial translation structures and uniform embeddings in groups
Property A, partial translation structures and uniform embeddings in groups
We define the concept of a partial translation structure T on a metric space X and we show that there is a natural C*-algebra C*(T) associated with it which is a subalgebra of the uniform Roe algebra C*u(X). We introduce a coarse invariant of the metric which provides an obstruction to embedding the space in a group. When the space is sufficiently group-like, as determined by our invariant, properties of the Roe algebra can be deduced from those of C*(T). We also give a proof of the fact that the uniform Roe algebra of a metric space is a coarse invariant up to Morita equivalence.
uniform roe algebra, exactness, partial translations, uniform embeddings, geometric group theory, coarse geometry
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd
18 October 2007
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd
Brodzki, Jacek, Niblo, Graham A. and Wright, Nick
(2007)
Property A, partial translation structures and uniform embeddings in groups.
Journal of the London Mathematical Society.
(doi:10.1112/jlms/jdm066).
Abstract
We define the concept of a partial translation structure T on a metric space X and we show that there is a natural C*-algebra C*(T) associated with it which is a subalgebra of the uniform Roe algebra C*u(X). We introduce a coarse invariant of the metric which provides an obstruction to embedding the space in a group. When the space is sufficiently group-like, as determined by our invariant, properties of the Roe algebra can be deduced from those of C*(T). We also give a proof of the fact that the uniform Roe algebra of a metric space is a coarse invariant up to Morita equivalence.
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- Accepted Manuscript
More information
Submitted date: 29 March 2006
Published date: 18 October 2007
Keywords:
uniform roe algebra, exactness, partial translations, uniform embeddings, geometric group theory, coarse geometry
Identifiers
Local EPrints ID: 44249
URI: http://eprints.soton.ac.uk/id/eprint/44249
ISSN: 0024-6107
PURE UUID: 9d3337a9-46ed-40e7-be2d-ca7ec5945d56
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Date deposited: 21 Feb 2007
Last modified: 16 Mar 2024 03:43
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