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.

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

Cited by in corpus (4)

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• 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