Hyperbolic groups acting improperly

Groves, Daniel¹ ; Manning, Jason Fox²

¹ Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL, United States
² Department of Mathematics, Cornell University, Ithaca, NY, United States

Geometry & topology, Tome 27 (2023) no. 9, pp. 3387-3460

Résumé

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.

Détail

DOI : 10.2140/gt.2023.27.3387

Classification : 20F65, 57M05
Keywords: hyperbolic groups, CAT(0) cube complexes

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