Relatively geometric actions on CAT(0) cube complexes

Abstract

We develop the foundations of the theory of relatively geometric actions of relatively hyperbolic groups on CAT(0) cube complexes, a notion introduced in our previous work [5]. In the relatively geometric setting we prove: full relatively quasi-convex subgroups are convex compact; an analog of Agol's Theorem; and a version of Haglund--Wise's Canonical Completion and Retraction.

arXiv comment19 pages, revised version to appear in J. Lond. Math. Soc

References in corpus (7)

• Relative hyperbolicity and relative quasiconvexity for countable groups
• Peripheral fillings of relatively hyperbolic groups
• Finiteness properties of cubulated groups
• Residual finiteness, QCERF, and fillings of hyperbolic groups
• Relatively hyperbolic groups: Intrinsic geometry, algebraic properties, and algorithmic problems
• Separation of Relatively Quasiconvex Subgroups
• Relative cubulations and groups with a 2-sphere boundary

Cited by in corpus (4)

• Relative cubulation of relative strict hyperbolization
• Cubulating a free-product-by-cyclic group
• Relatively geometric actions of Kähler groups on CAT(0) cube complexes
• Quasiconvexity of virtual joins and separability of products in relatively hyperbolic groups