Small cancellation in acylindrically hyperbolic groups

  • Michael Hull

    University of Illinois-Urbana Champaign, USA


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.

Cite this article

Michael Hull, Small cancellation in acylindrically hyperbolic groups. Groups Geom. Dyn. 10 (2016), no. 4, pp. 1077–1119

DOI 10.4171/GGD/377