Hyperbolic groups acting improperly

Groves, Daniel; Manning, Jason Fox

doi:10.2140/gt.2023.27.3387

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Hyperbolic groups acting improperly

Daniel Groves and Jason Fox Manning

Geometry & Topology 27 (2023) 3387–3460

DOI: 10.2140/gt.2023.27.3387

Abstract

We study hyperbolic groups acting on CAT $(0)$ cube complexes. The first main result is a structural result about the Sageev construction, in which we relate quasiconvexity of hyperplane stabilizers with quasiconvexity of cell stabilizers. The second main result generalizes both Agol’s Theorem on cubulated hyperbolic groups and Wise’s Quasiconvex Hierarchy Theorem.

Keywords

hyperbolic groups, CAT(0) cube complexes

Mathematical Subject Classification 2010

Primary: 20F65, 57M05

References

Publication

Received: 29 April 2019

Revised: 14 March 2021

Accepted: 14 June 2022

Published: 5 December 2023

Proposed: Martin R Bridson

Seconded: Benson Farb, Bruce Kleiner

Authors

Daniel Groves
Department of Mathematics, Statistics and Computer Science University of Illinois at Chicago Chicago, IL United States

Jason Fox Manning
Department of Mathematics Cornell University Ithaca, NY United States

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Volume 27, issue 9 (2023)