Boundary amenability of $Out(F_N)$

Abstract

We prove that $Out(F_N)$ is boundary amenable. This also holds more generally for $Out(G)$, where $G$ is either a toral relatively hyperbolic group or a finitely generated right-angled Artin group. As a consequence, all these groups satisfy the Novikov conjecture on higher signatures.

arXiv commentv2: Final version. Accepted in Annales scientifiques de l'École normale supérieure