Acylindrical Hyperbolicity of $Out(W_n)$ - Healy, Brendan Burns (Topology Proceedings, 2020)
We prove that the group of outer automorphisms of the free Coxeter group $W_n$ is acylindrically hyperbolic in the sense of Osin. We observe that any $CAT(0)$ space admitting a geometric action by $Out(W_n)$ must contain a rank-one geodesic as an application. Our main theorem proceeds from expanding on a well-known relationship between $Out(W_n)$ and the outer automorphism group of free groups.