Hyperbolic groups acting improperly

Abstract

In this paper we study hyperbolic groups acting on CAT(0) cube complexes. The first main result (Theorem A) is a structural result about the Sageev construction, in which we relate quasi-convexity of hyperplane stabilizers with quasi-convexity of cell stabilizers. The second main result (Theorem D) generalizes both Agol's theorem on cubulated hyperbolic groups and Wise's Quasi-convex Hierarchy Theorem.

54pp. v5 is the accepted version. To appear in Geometry and Topology

References in corpus (4)

• On strongly quasiconvex subgroups
• Ubiquitous quasi-Fuchsian surfaces in cusped hyperbolic 3-manifolds
• Relative cubulations and groups with a 2-sphere boundary
• Boundaries of Dehn fillings

Cited by in corpus (5)

• Relative cubulations and groups with a 2-sphere boundary
• Special cubulation of strict hyperbolization
• Relative cubulation of relative strict hyperbolization
• Cubulating a free-product-by-cyclic group
• Relatively geometric actions of Kähler groups on CAT(0) cube complexes