Centralisers of linear growth automorphisms of free groups
Centralisers of linear growth automorphisms of free groups
In this note we investigate the centraliser of a linearly growing element of Out(Fn) (that is, a root of a Dehn twist automorphism), and show that it has a finite index subgroup mapping onto a direct product of certain "equivariant McCool groups" with kernel a finitely generated free abelian group. In particular, this allows us to show it is VF and hence finitely presented.
math.GR, 20E36 (Primary) 20E05, 20E08 (Secondary)
Andrew, Naomi
abf231d3-cbd0-4d67-834b-e249ce554108
Martino, Armando
65f1ff81-7659-4543-8ee2-0a109be286f1
Andrew, Naomi
abf231d3-cbd0-4d67-834b-e249ce554108
Martino, Armando
65f1ff81-7659-4543-8ee2-0a109be286f1
[Unknown type: UNSPECIFIED]
Abstract
In this note we investigate the centraliser of a linearly growing element of Out(Fn) (that is, a root of a Dehn twist automorphism), and show that it has a finite index subgroup mapping onto a direct product of certain "equivariant McCool groups" with kernel a finitely generated free abelian group. In particular, this allows us to show it is VF and hence finitely presented.
Text
2205.12865v1
- Author's Original
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Submitted date: 25 May 2022
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20 pages, 2 figures
Keywords:
math.GR, 20E36 (Primary) 20E05, 20E08 (Secondary)
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Local EPrints ID: 473088
URI: http://eprints.soton.ac.uk/id/eprint/473088
PURE UUID: fc6a7cb0-0c27-4203-bd0b-ea6fe13ff213
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Date deposited: 10 Jan 2023 18:02
Last modified: 17 Mar 2024 03:16
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Author:
Naomi Andrew
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