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 \(n\ge 4\) the group of symmetries of the spine of the Guirardel-Levitt outer space of \(W_n\) is reduced to the outer automorphism group \({\mathrm {Out}}(W_n)\).