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.
Citation
Max Forester. Ignat Soroko. Jing Tao. "Genus bounds in right-angled Artin groups." Publ. Mat. 64 (1) 233 - 253, 2020. https://doi.org/10.5565/PUBLMAT6412010
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