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Genus bounds in right-angled Artin groups (1710.10542v2)
Published 29 Oct 2017 in math.GR and math.GT
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.
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