#### Volume 21, issue 3 (2021)

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Powers of Dehn twists generating right-angled Artin groups

### Donggyun Seo

Algebraic & Geometric Topology 21 (2021) 1511–1533
##### Abstract

We give a bound for the exponents of powers of Dehn twists to generate a right-angled Artin group. Precisely, if $\mathsc{ℱ}$ is a finite collection of pairwise distinct simple closed curves on a surface and if $N$ denotes the maximum of the intersection numbers of all pairs of curves in $\mathsc{ℱ}$, then we prove that $\left\{{T}_{\gamma }^{n}\mid \gamma \in \mathsc{ℱ}\right\}$ generates a right-angled Artin group for all $n\ge {N}^{2}+N+3$. This extends a previous result of Koberda, who proved the existence of a bound possibly depending on the underlying hyperbolic structure of the surface. In the course of the proof, we obtain a universal bound depending only on the topological type of the surface in certain cases, which partially answers a question due to Koberda.

##### Keywords
Dehn twist, right-angled Artin group, mapping class group
##### Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 20E08, 57M60