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

We give a bound for the exponents of powers of Dehn twists to generate a right-angled Artin group. Precisely, if 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 , then we prove that {Tγnγ } generates a right-angled Artin group for all n N2 + 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.

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Dehn twist, right-angled Artin group, mapping class group
Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 20E08, 57M60
Received: 10 December 2019
Revised: 29 April 2020
Accepted: 3 June 2020
Published: 11 August 2021
Donggyun Seo
School of Mathematics
Korea Institute for Advanced Study
South Korea