Small cancellation in acylindrically hyperbolic groups

2013/08/20 by Michael Hull, Hull, M. · 5 citations
Mathematics · #20F06 #20F65 #20F67 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1308.4345

openalex publication_date 2013/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Stability, approximable quotients, and higher property (T)
• Boundary actions of CAT(0) spaces: topological freeness and applications to C^*-algebras
• Cubical small-cancellation quotients of non-products
• On automorphisms, quasimorphisms, and coarse automorphisms of acylindrically hyperbolic groups
• First-order aspects of Artin groups

Related

• Groups acting acylindrically on hyperbolic spaces
• Small cancellation and outer automorphisms of Kazhdan groups acting on hyperbolic spaces
• Infinitely presented graphical small cancellation groups are acylindrically hyperbolic
• Acylindrically hyperbolic groups
• Actions of small cancellation groups on hyperbolic spaces