Osaka Journal of Mathematics

Right-angled Artin groups and finite subgraphs of curve graphs

Sang-Hyun Kim and Thomas Koberda

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 5 August 2016

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1470413985

Mathematical Reviews number (MathSciNet)
MR3533464

Zentralblatt MATH identifier
06629520

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

Citation

Kim, Sang-Hyun; Koberda, Thomas. Right-angled Artin groups and finite subgraphs of curve graphs. Osaka J. Math. 53 (2016), no. 3, 705--716. https://projecteuclid.org/euclid.ojm/1470413985


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