Commensurations of the outer automorphism group of a universal Coxeter group

Groups, geometry, and dynamics

article

Yassine Guerch¹ 

[1] Université Paris-Saclay

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

DOI  :  10.4171/ggd/718

学科分类：神经科学

来源: European Mathematical Society

【 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​).

【 授权许可】

CC BY