Extensions of multicurve stabilizers are hierarchically hyperbolic

Abstract

For a closed and orientable surface of genus at least 2, we prove the surface group extensions of the stabilizers of multicurves are hierarchically hyperbolic groups. This answers a question of Durham, Dowdall, Leininger, and Sisto. We also include an appendix that employs work of Charney, Cordes, and Sisto to characterize the Morse boundaries of hierarchically hyperbolic groups whose largest acylindrical action on a hyperbolic space is on a quasi-tree.

Version accepted to Geometry & Topology

References in corpus (2)

• Stable Subgroups of the Genus Two Handlebody Group
• Extensions of Veech groups II: Hierarchical hyperbolicity and quasi-isometric rigidity

Cited by in corpus (1)

• A Combinatorial Structure for Many Hierarchically Hyperbolic Spaces