Acylindrical group actions on quasi-trees

Abstract

A group G is acylindrically hyperbolic if it admits a non-elementary acylindrical action on a hyperbolic space. We prove that every acylindrically hyperbolic group G has a generating set X such that the corresponding Cayley graph is a (non-elementary) quasi-tree and the action of G on the Cayley graph is acylindrical. Our proof utilizes the notions of hyperbolically embedded subgroups and projection complexes. As a by-product, we obtain some new results about hyperbolically embedded subgroups and quasi-convex subgroups of acylindrically hyperbolic groups.

References in corpus (1)

• On acylindrical hyperbolicity of groups with positive first ${\ell }^2$-Betti number

Cited by in corpus (6)

• Random walks, WPD actions, and the Cremona group
• A dynamical characterization of acylindrically hyperbolic groups
• Hyperbolicity and uniformly Lipschitz affine actions on subspaces of $L^1$
• Acylindrical hyperbolicity of cubical small-cancellation groups
• Groups Acting Acylindrically on Trees
• Product set growth in virtual subgroups of mapping class groups