Groups Acting Acylindrically on Trees

Abstract

We develop a notion of groups that act acylindrically and non-elementarily on simplicial trees, which we call acylindrically arboreal groups. We then prove a complete classification of when graph products of groups and the fundamental groups of certain hyperbolic $3$-manifolds are acylindrically arboreal, and use these classifications to provide examples of acylindrically hyperbolic groups that have actions on trees but have no non-elementary acylindrical actions on trees.

Version to appear in Journal of Group Theory. 27 Pages, 2 figures

References in corpus (6)

• Relative hyperbolicity and relative quasiconvexity for countable groups
• Induced quasi-cocycles on groups with hyperbolically embedded subgroups
• Groups acting on CAT(0) cube complexes
• Packing subgroups in relatively hyperbolic groups
• Acylindrical group actions on quasi-trees
• On equationally Noetherian and residually finite groups