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

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.

v2: 60 pages, 10 figures. This is the sequel to arXiv:2006.16425. Updates to incorporate referee comments. Final version accepted for publication in Commentarii Mathematici Helvetici

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Cited by in corpus (2)

• Extensions of multicurve stabilizers are hierarchically hyperbolic
• A Combinatorial Structure for Many Hierarchically Hyperbolic Spaces