Genus bounds in right-angled Artin groups

Abstract

We show that in any right-angled Artin group whose defining graph has chromatic number $k$, every non-trivial element has stable commutator length at least $1/(6k)$. Secondly, if the defining graph does not contain triangles, then every non-trivial element has stable commutator length at least $1/20$. These results are obtained via an elementary geometric argument based on earlier work of Culler.

V.2: a second main theorem was added and the title changed. 16 pages, 4 figures. V.1: 14 pages, 4 figures