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arXiv · 2205.12865

Centralisers of linear growth automorphisms of free groups

Naomi Andrew·Armando Martino
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Abstract

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

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Naomi Andrew, Armando Martino. 2022-05-25. Centralisers of linear growth automorphisms of free groups. https://doi.org/10.1017/s0305004124000203

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