# Boundary amenability of $Out(F_N)$

## TL;DR

This paper proves that the outer automorphism groups of free groups and certain other groups are boundary amenable, implying they satisfy the Novikov conjecture on higher signatures, which has significant implications in topology.

## Contribution

The paper establishes boundary amenability for $Out(F_N)$ and related groups, extending previous results to a broader class of groups.

## Key findings

- $Out(F_N)$ is boundary amenable.
- Boundary amenability extends to $Out(G)$ for certain groups.
- These groups satisfy the Novikov conjecture.

## 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.