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arXiv · 1710.10542

Genus bounds in right-angled Artin groups

Max Forester·Ignat Soroko·Jing Tao
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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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Max Forester, Ignat Soroko, Jing Tao. 2017-10-29. Genus bounds in right-angled Artin groups. https://doi.org/10.5565/publmat6412010

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