Acylindrical Hyperbolicity of Out($W_n$)
Group Theory
2020-09-22 v5
Abstract
We prove that the group of outer automorphisms of the free Coxeter group is acylindrically hyperbolic in the sense of Osin. As an application, we observe that any CAT(0) space admitting a geometric action by Out() must contain a rank-one geodesic. The theorem proceeds from expanding on a well-known relationship between Out() and the outer automorphism group of free groups.
Cite
@article{arxiv.1610.08005,
title = {Acylindrical Hyperbolicity of Out($W_n$)},
author = {Brendan Burns Healy},
journal= {arXiv preprint arXiv:1610.08005},
year = {2020}
}