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Commensurating HNN
extensions: nonpositive curvature and biautomaticity
Ian J Leary and Ashot Minasyan |
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Geometry & Topology 25 (2021) 1819–1860
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Abstract |
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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 but not biautomatic. These groups also resolve a number of other questions concerning groups. |
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Keywords
commensurating HNN extension, biautomatic group, CAT(0)
group
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Mathematical Subject Classification 2010
Primary: 20F10, 20F67
Secondary: 20E06
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References |
Publication
Received: 23 July 2019
Revised: 18 June 2020
Accepted: 20 June 2020
Published: 12 July 2021
Proposed: Ian Agol
Seconded: Mladen Bestvina, Benson Farb
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Authors |
| Ian J Leary | |
| School of Mathematical
Sciences University of Southampton Southampton United Kingdom |
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| Ashot Minasyan | |
| School of Mathematical
Sciences University of Southampton Southampton United Kingdom |
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