Extensions of multicurve stabilizers are hierarchically hyperbolic

Russell, Jacob

doi:10.2140/gt.2025.29.3187

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Extensions of multicurve stabilizers are hierarchically hyperbolic

Jacob Russell

Geometry & Topology 29 (2025) 3187–3240

DOI: 10.2140/gt.2025.29.3187

Abstract

For a closed and orientable surface $S$ with genus at least 2, we prove that the $π_{1} (S)$ -extensions of the stabilizers of multicurves on $S$ 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 quasitree.

Keywords

mapping class groups, geometric finiteness

Mathematical Subject Classification

Primary: 20F65, 20F67, 57K20

References

Publication

Received: 26 October 2021

Revised: 19 September 2023

Accepted: 30 December 2024

Published: 22 September 2025

Proposed: Martin R Bridson

Seconded: Benson Farb, David Fisher

Authors

Jacob Russell
Department of Mathematics and Statistics Swarthmore College Swarthmore, PA United States

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Volume 29, issue 6 (2025)