Small cancellation in acylindrically hyperbolic groups

Abstract

We generalize a version of small cancellation theory to the class of acylindrically hyperbolic groups. This class contains many groups which admit some natural action on a hyperbolic space, including non-elementary hyperbolic and relatively hyperbolic groups, mapping class groups, and groups of outer automorphisms of free groups. Several applications of this small cancellation theory are given, including to Frattini subgroups and Kazhdan constants, the construction of various \exotic"' quotients, and to approximating acylindrically hyperbolic groups in the topology of marked group presentations.

36 pages

References in corpus (1)

• On topologizable and non-topologizable groups

Cited by in corpus (7)

• On topologizable and non-topologizable groups
• On acylindrical hyperbolicity of groups with positive first ${\ell }^2$-Betti number
• Extending higher dimensional quasi-cocycles
• Formal conjugacy growth in acylindrically hyperbolic groups
• Transitivity degrees of countable groups and acylindrical hyperbolicity
• On purely loxodromic actions
• Non-elementary convergence groups are acylindrically hyperbolic