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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 showthat it has a finite index subgroup mapping onto a direct product of certain"equivariant McCool groups" with kernel a finitely generated free abeliangroup. In particular, this allows us to show it is VF and hence finitelypresented.

Centralisers of linear growth automorphisms of free groups