Finite asymptotic dimension for CAT(0) cube complexes
Finite asymptotic dimension for CAT(0) cube complexes
We prove that the asymptotic dimension of a finite-dimensional CAT(0) cube complex is bounded above by the dimension. To achieve this we prove a controlled colouring theorem for the complex. We also show that every CAT(0) cube complex is a contractive retraction of an infinite dimensional cube. As an example of the dimension theorem we obtain bounds on the asymptotic dimension of small cancellation groups.
asymptotic dimension, CAT(0) cube complex, small cancellation group
527-554
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd
8 April 2012
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd
Wright, Nick
(2012)
Finite asymptotic dimension for CAT(0) cube complexes.
Geometry & Topology, 16 (1), .
(doi:10.2140/gt.2012.16.527).
Abstract
We prove that the asymptotic dimension of a finite-dimensional CAT(0) cube complex is bounded above by the dimension. To achieve this we prove a controlled colouring theorem for the complex. We also show that every CAT(0) cube complex is a contractive retraction of an infinite dimensional cube. As an example of the dimension theorem we obtain bounds on the asymptotic dimension of small cancellation groups.
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1004.4172v1
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Other
1004.4172v1
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More information
Published date: 8 April 2012
Keywords:
asymptotic dimension, CAT(0) cube complex, small cancellation group
Organisations:
Pure Mathematics
Identifiers
Local EPrints ID: 147377
URI: http://eprints.soton.ac.uk/id/eprint/147377
ISSN: 1465-3060
PURE UUID: 9b4af264-62c8-400a-9ef8-0b33fd66e1ee
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Date deposited: 10 May 2010 13:08
Last modified: 14 Mar 2024 02:50
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