Infinite groups acting faithfully on the outer automorphism group of a right-angled Artin group
Group Theory
2015-07-17 v1
Abstract
We construct the first known examples of infinite subgroups of the outer automorphism group of Out(A_Gamma), for certain right-angled Artin groups A_Gamma. This is achieved by introducing a new class of graphs, called focused graphs, whose properties allow us to exhibit (infinite) projective linear groups as subgroups of Out(Out(A_Gamma)). This demonstrates a marked departure from the known behavior of Out(Out(A_Gamma)) when A_Gamma is free or free abelian, as in these cases Out(Out(A_Gamma)) has order at most 4. We also disprove a previous conjecture of the second author, producing new examples of finite order members of certain Out(Aut(A_Gamma)).
Keywords
Cite
@article{arxiv.1507.04359,
title = {Infinite groups acting faithfully on the outer automorphism group of a right-angled Artin group},
author = {Corey Bregman and Neil J. Fullarton},
journal= {arXiv preprint arXiv:1507.04359},
year = {2015}
}