Commensurations of the outer automorphism group of a universal Coxeter group

[摘要] This paper studies the rigidity properties of the abstract commensurator of the outer automorphism group of a universal Coxeter group of rank nnn, which is the free product WnW_nWn​ of nnn copies of Z/2Z\mathbb{Z}/2\mathbb{Z}Z/2Z. We prove that for n≥5n\geq 5n≥5 the natural map Out(Wn)→Comm(Out(Wn))\mathrm{Out}(W_n) \to \mathrm{Comm}(\mathrm{Out}(W_n))Out(Wn​)→Comm(Out(Wn​)) is an isomorphism and that every isomorphism between finite index subgroups of Out(Wn)\mathrm{Out}(W_n)Out(Wn​) is given by a conjugation by an element of Out(Wn)\mathrm{Out}(W_n)Out(Wn​).

[学科分类] 神经科学

[关键词] Universal Coxeter group;outer automorphism groups;abstract commensurator;outer space;group actions on trees