Boundary amenability of $Out(F_N)$

Mladen Bestvina (1) , Vincent Guirardel (2) , Camille Horbez (3)

1 Department of Mathematics - University of Utah
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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 right-angled Artin group. As a consequence, all these groups satisfy the Novikov conjecture on higher signatures.

Domaines: Théorie des groupes [math.GR]; Topologie géométrique [math.GT]; Algèbres d'opérateurs [math.OA]

Mladen Bestvina, Vincent Guirardel, Camille Horbez. Boundary amenability of $Out(F_N)$. Annales Scientifiques de l'École Normale Supérieure, 2022, 55 (5), pp.1379-1431. ⟨10.24033/asens.2519⟩. ⟨hal-01535620⟩