Powers of Dehn twists generating right-angled Artin groups

Abstract

We give a bound for the exponents of powers of Dehn twists to generate a right-angled Artin group. Precisely, if $\mathcal{F}$ is a finite collection of pairwise distinct simple closed curves on a finite type surface and if $N$ denotes the maximum of the intersection numbers of all pairs of curves in $\mathcal{F}$, then we prove that $\{T_{\gamma }^n|\gamma \in \mathcal{F}\}$ 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.

16 pages, 8 figures

Cited by in corpus (3)

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