Abstract commensurators of right-angled Artin groups and mapping class groups
Geometric Topology
2014-03-19 v2 Group Theory
Abstract
We prove that, aside from the obvious exceptions, the mapping class group of a compact orientable surface is not abstractly commensurable with any right-angled Artin group. Our argument applies to various subgroups of the mapping class group---the subgroups generated by powers of Dehn twists and the terms of the Johnson filtration---and additionally to the outer automorphism group of a free group and to certain linear groups.
Keywords
Cite
@article{arxiv.1307.8387,
title = {Abstract commensurators of right-angled Artin groups and mapping class groups},
author = {Matt Clay and Christopher J. Leininger and Dan Margalit},
journal= {arXiv preprint arXiv:1307.8387},
year = {2014}
}
Comments
8 pages; incorporates referee comments