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The geometry of cube complexes and the complexity of their fundamental groups

The geometry of cube complexes and the complexity of their fundamental groups
The geometry of cube complexes and the complexity of their fundamental groups
We investigate the geometry of geodesics in CAT(0) cube complexes. A group which acts cocompactly and properly discontinuously on such a complex is shown to have a biautomatic structure. There is a family of natural subgroups each of which is shown to be rational.
biautomatic groups, CAT(0) cube complexes, non-positive curvature
0040-9383
621-633
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Reeves, Lawrence D.
84a70e26-d717-4909-ad72-4c79581b3ccd
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Reeves, Lawrence D.
84a70e26-d717-4909-ad72-4c79581b3ccd

Niblo, Graham A. and Reeves, Lawrence D. (1998) The geometry of cube complexes and the complexity of their fundamental groups. Topology, 37 (3), 621-633. (doi:10.1016/S0040-9383(97)00018-9).

Record type: Article

Abstract

We investigate the geometry of geodesics in CAT(0) cube complexes. A group which acts cocompactly and properly discontinuously on such a complex is shown to have a biautomatic structure. There is a family of natural subgroups each of which is shown to be rational.

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More information

Published date: May 1998
Keywords: biautomatic groups, CAT(0) cube complexes, non-positive curvature

Identifiers

Local EPrints ID: 49987
URI: https://eprints.soton.ac.uk/id/eprint/49987
ISSN: 0040-9383
PURE UUID: 1052ed3a-daf8-483e-87d3-64f54a6b33f1

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Date deposited: 10 Jan 2008
Last modified: 17 Jul 2017 14:54

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Contributors

Author: Graham A. Niblo
Author: Lawrence D. Reeves

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