Small cancellation in acylindrically hyperbolic groups
By Michael Hull. 2013
59 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a7aeba35c691fe0c808b119cd907ecde7bc5aaa2
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In Geometry and Topology
- Michael Hull
- Denis V. Osin
- Alessandro Sisto
- Ashot Minasyan
- Anthony Genevois
- Jason A. Behrstock
- Mark F. Hagen
- Vincent Guirardel
In Mathematical Physics
- Denis V. Osin
- Michael Hull
- Alessandro Sisto
- Mark F. Hagen
- Anthony Genevois
- Ashot Minasyan
- Vincent Guirardel
- Franccois Dahmani
Citations in the corpus
- Acylindrically hyperbolic groups (2013, background): “Theorem 8.6 (Hull [29]) .”
- GROUPS ACTING ACYLINDRICALLY ON HYPERBOLIC SPACES (2017, result): “Yet another result proved by Hull and Osin [2016a] is the following.”
- Transitivity degrees of countable groups and acylindrical hyperbolicity (2015, methodology): “erbolic groups, so we choose another approach based on the notion of a small subgroup introduced in the previous section and small cancellation theory in acylindrically hyperbolic groups developed in [32]. More precisely, we prove in Lemma 3.1 that if H i is small for some i, then by choosing the el”
- Acylindrical hyperbolicity of groups acting on trees (2013, unknown): “His main result covers many classical theorems about random elements of hyperbolic groups, mapping class groups, etc. • Yet another direction is explored by Hull [48], who developed a version of small cancellation theory for acylindrically hyperbolic groups and used it to construct groups with certa”