English

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 kk, every non-trivial element has stable commutator length at least 1/(6k)1/(6k). Secondly, if the defining graph does not contain triangles, then every non-trivial element has stable commutator length at least 1/201/20. 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

R2 v1 2026-06-22T22:28:40.757Z