Extensions of Veech groups II: Hierarchical hyperbolicity and quasi-isometric rigidity

Spencer Dowdall; Matthew G. Durham; Christopher J. Leininger; Alessandro Sisto

doi:10.4171/cmh/568

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arXiv · 2111.00685

Extensions of Veech groups II: Hierarchical hyperbolicity and quasi-isometric rigidity

Spencer Dowdall·Matthew G. Durham·Christopher J. Leininger·Alessandro Sisto

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Abstract

We show that for any lattice Veech group in the mapping class group $\mathrm{Mod}(S)$ of a closed surface $S$, the associated $\pi_1 S$--extension group is a hierarchically hyperbolic group. As a consequence, we prove that any such extension group is quasi-isometrically rigid.

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Spencer Dowdall, Matthew G. Durham, Christopher J. Leininger, Alessandro Sisto. 2021-11-01. Extensions of Veech groups II: Hierarchical hyperbolicity and quasi-isometric rigidity. https://doi.org/10.4171/cmh/568

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