Centralisers and the virtually cyclic dimension of $\mathrm{Out}(F_N)$

Yassine Guerch, Sam Hughes, Luis Jorge Sánchez Saldaña

We prove that the virtually cyclic (geometric) dimension of the finite index congruence subgroup ${\mathrm{IA}}_N(3)$ of $\mathrm{Out}(F_N)$ is $2N-2$. From this we deduce the virtua…