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

JournalscmhVol. 99, No. 1pp. 149–228

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

Spencer Dowdall
Vanderbilt University, Nashville, USA
Matthew G. Durham
University of California, Riverside, USA
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Christopher J. Leininger
Rice University, Houston, USA
Alessandro Sisto
Heriot-Watt University, Edinburgh, UK

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Abstract

We show that for any lattice Veech group in the mapping class group $M o d (S)$ of a closed surface $S$ , the associated $π_{1} S$ -extension group is a hierarchically hyperbolic group. As a consequence, we prove that any such extension group is quasi-isometrically rigid.

Cite this article

Spencer Dowdall, Matthew G. Durham, Christopher J. Leininger, Alessandro Sisto, Extensions of Veech groups II: Hierarchical hyperbolicity and quasi-isometric rigidity. Comment. Math. Helv. 99 (2024), no. 1, pp. 149–228

DOI 10.4171/CMH/568