Osaka Journal of Mathematics

Right-angled Artin groups and finite subgraphs of curve graphs

Sang-Hyun Kim and Thomas Koberda

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We show that for a sufficiently simple surface $S$, if a right-angled Artin group $A(\Gamma)$ embeds into $\mathrm{Mod}(S)$ then $\Gamma$ embeds into the curve graph $\mathcal{C}(S)$ as an induced subgraph. When $S$ is sufficiently complicated, there exists an embedding $A(\Gamma) \to \mathrm{Mod}(S)$ such that $\Gamma$ is not contained in $\mathcal{C}(S)$ as an induced subgraph.

Article information

Osaka J. Math., Volume 53, Number 3 (2016), 705-716.

First available in Project Euclid: 5 August 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F36: Braid groups; Artin groups 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]


Kim, Sang-Hyun; Koberda, Thomas. Right-angled Artin groups and finite subgraphs of curve graphs. Osaka J. Math. 53 (2016), no. 3, 705--716.

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