Relative cubulations and groups with a 2-sphere boundary

Abstract

We introduce a new kind of action of a relatively hyperbolic group on a CAT(0) cube complex, called a relatively geometric action. We provide an application to characterize finite-volume Kleinian groups in terms of action on cube complexes, analogous to the results of Markovic and Haïssinsky in the closed case.

arXiv comment5 pages

References in corpus (6)

• Relative hyperbolicity and relative quasiconvexity for countable groups
• Finiteness properties of cubulated groups
• Residual finiteness, QCERF, and fillings of hyperbolic groups
• Ubiquitous quasi-Fuchsian surfaces in cusped hyperbolic 3-manifolds
• Hyperbolic groups acting improperly
• Boundaries of Dehn fillings

Cited by in corpus (6)

• Hyperbolic groups acting improperly
• Relatively geometric actions on CAT(0) cube complexes
• Relative cubulation of relative strict hyperbolization
• Cubulating a free-product-by-cyclic group
• Relatively geometric actions of Kähler groups on CAT(0) cube complexes
• Relative Cubulation of Small Cancellation Free Products