Commensurations of $\mathrm{Aut}(F_N)$ and its Torelli subgroup

Abstract

For $N\ge 3$, the abstract commensurators of both $\mathrm{Aut}(F_N)$ and its Torelli subgroup ${\mathrm{IA}}_N$ are isomorphic to $\mathrm{Aut}(F_N)$ itself.

30 pages, 5 figures. Version accepted to appear in GAFA

Cited by in corpus (3)

• Direct products of free groups in $\mathrm{Aut}(F_N)$
• Effective finite generation for [IA_n,IA_n] and the Johnson kernel
• Higher incoherence of the automorphism groups of a free group