Groups, Geometry, and Dynamics

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Volume 10, Issue 4, 2016, pp. 1077–1119
DOI: 10.4171/GGD/377

Published online: 2017-01-26

Small cancellation in acylindrically hyperbolic groups

Michael Hull[1]

(1) 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.

Keywords: Small cancellation theory, acylindrically hyperbolic groups

Hull Michael: Small cancellation in acylindrically hyperbolic groups. Groups Geom. Dyn. 10 (2016), 1077-1119. doi: 10.4171/GGD/377