Commensurating HNN-extensions: non-positive curvature and biautomaticity
Commensurating HNN-extensions: non-positive curvature and biautomaticity
We show that the commensurator of any quasiconvex abelian subgroup in a biautomatic group is small, in the sense that it has finite image in the abstract commensurator of the subgroup. Using this criterion we exhibit groups that are CAT(0) but not biautomatic. These groups also resolve a number of other questions concerning CAT(0) groups.
1819–1860
Leary, Ian
57bd5c53-cd99-41f9-b02a-4a512d45150e
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
12 July 2021
Leary, Ian
57bd5c53-cd99-41f9-b02a-4a512d45150e
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
Leary, Ian and Minasyan, Ashot
(2021)
Commensurating HNN-extensions: non-positive curvature and biautomaticity.
Geometry & Topology, 25 (4), .
Abstract
We show that the commensurator of any quasiconvex abelian subgroup in a biautomatic group is small, in the sense that it has finite image in the abstract commensurator of the subgroup. Using this criterion we exhibit groups that are CAT(0) but not biautomatic. These groups also resolve a number of other questions concerning CAT(0) groups.
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biaut-7
- Author's Original
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biaut-11
- Accepted Manuscript
More information
In preparation date: 9 July 2019
Accepted/In Press date: 20 June 2020
Published date: 12 July 2021
Identifiers
Local EPrints ID: 432346
URI: http://eprints.soton.ac.uk/id/eprint/432346
ISSN: 1465-3060
PURE UUID: 453b5de9-c922-453a-894a-1c0bca963fc8
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Date deposited: 11 Jul 2019 16:30
Last modified: 16 Mar 2024 08:01
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