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Hyperbolic groups acting improperly

Daniel Groves and Jason Fox Manning

Geometry & Topology 27 (2023) 3387–3460
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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