Genus bounds in right-angled Artin groups
Group Theory
2020-03-03 v2 Geometric Topology
Abstract
We show that in any right-angled Artin group whose defining graph has chromatic number , every non-trivial element has stable commutator length at least . Secondly, if the defining graph does not contain triangles, then every non-trivial element has stable commutator length at least . These results are obtained via an elementary geometric argument based on earlier work of Culler.
Keywords
Cite
@article{arxiv.1710.10542,
title = {Genus bounds in right-angled Artin groups},
author = {Max Forester and Ignat Soroko and Jing Tao},
journal= {arXiv preprint arXiv:1710.10542},
year = {2020}
}
Comments
V.2: a second main theorem was added and the title changed. 16 pages, 4 figures. V.1: 14 pages, 4 figures