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Effective generation of right-angled artin groups in mapping class groups

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Abstract

We show that given a collection \(X=\{f_1\), ..., \(f_m\}\) of pure mapping classes on a surface S, there is an explicit constant N, depending only on X, such that their Nth powers \(\{f_1^N\), ..., \(f_m^N\}\) generate the expected right-angled Artin subgroup of MCG(S). Moreover, we show that these subgroups are undistorted, and that each element is pseudo-Anosov on the largest possible subsurface.

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Acknowledgements

The author would like to thank Thomas Koberda, Marissa Loving, and Johanna Mangahas for insightful conversations. The author would also like to thank Jason Behrstock, George Domat, and Rylee Lyman for constructive feedback on an early draft of this paper. Finally, the author thanks the anonymous referee for numerous suggestions which vastly improved the quality of this paper.

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  1. University of Virginia, Charlottesville, VA, USA

    Ian Runnels

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  1. Ian Runnels
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Runnels, I. Effective generation of right-angled artin groups in mapping class groups. Geom Dedicata 214, 277–294 (2021). https://doi.org/10.1007/s10711-021-00615-0

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