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Centralisers of linear growth automorphisms of free groups

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)
0305-0041
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

Andrew, Naomi and Martino, Armando (2024) Centralisers of linear growth automorphisms of free groups. Mathematical Proceedings of the Cambridge Philosophical Society. (doi:10.1017/S0305004124000203).

Record type: Article

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.

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Submitted date: 25 May 2022
Accepted/In Press date: 15 February 2024
e-pub ahead of print date: 20 September 2024
Keywords: math.GR, 20E36 (Primary) 20E05, 20E08 (Secondary)
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Identifiers

Local EPrints ID: 473088
URI: http://eprints.soton.ac.uk/id/eprint/473088
DOI: doi:10.1017/S0305004124000203
ISSN: 0305-0041
PURE UUID: fc6a7cb0-0c27-4203-bd0b-ea6fe13ff213
ORCID for Armando Martino: ORCID iD orcid.org/0000-0002-5350-3029

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Date deposited: 10 Jan 2023 18:02
Last modified: 21 Sep 2024 01:44

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Contributors

Author: Naomi Andrew
Author: Armando Martino ORCID iD

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