English

Centralisers of linear growth automorphisms of free groups

Group Theory 2024-12-11 v2

Abstract

In this note we investigate the centraliser of a linearly growing element of Out(Fn)\mathrm{Out}(F_n) (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.

Keywords

Cite

@article{arxiv.2205.12865,
  title  = {Centralisers of linear growth automorphisms of free groups},
  author = {Naomi Andrew and Armando Martino},
  journal= {arXiv preprint arXiv:2205.12865},
  year   = {2024}
}

Comments

23 pages, 2 figures; v2: final version, to appear in Mathematical Proceedings of the Cambridge Philosophical Society; new introduction and some reordering