Finiteness properties of centralisers in $\mathrm{Out}(F_N)$ and automorphisms of free-by-cyclic groups

Naomi Andrew, Yassine Guerch, Camille Horbez +1

Let $F$ be a finitely generated free group. We prove that the centraliser of any element of $\mathrm{Out}(F)$ or $\mathrm{Aut}(F)$ is of type $\mathrm{VF}$. We also prove that the (out…