The symmetries of the Outer space of a universal Coxeter group

Abstract

This paper studies the geometric rigidity of the universal Coxeter group of rank $n$, which is the free product $W_n$ of $n$ copies of $\mathbb{Z}/2\mathbb{Z}$. We prove that for $n\geq 4$ the group of symmetries of the spine of the Guirardel-Levitt outer space of $W_n$ is reduced to the outer automorphism group $\mathrm{Out}(W_n)$.