GROUPS ACTING ACYLINDRICALLY ON HYPERBOLIC SPACES
By Denis V. Osin. International Congress of Mathematicans, 2017
62 citations recorded by the source corpus.
The goal of this article is to survey some recent developments in the study of groups acting on hyperbolic spaces. We focus on the class of acylindrically hyperbolic groups; it is broad enough to include many examples of interest, yet a significant part of the theory of hyperbolic and relatively hyperbolic groups can be generalized in this context. In particular, we discuss group theoretic Dehn filling and small cancellation theory in acylindrically hyperbolic groups. Many results discussed here rely on the new generalization of relative hyperbolicity based on the notion of a hyperbolically embedded subgroup.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/6fdac6aeffd855e59d9e728182e96e13b54998f1
How researchers see this paper
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In Discrete Mathematics and Combinatorics
- Anthony Genevois
- Carolyn R. Abbott
- Alexandre Martin
- S. Balasubramanya
- Denis V. Osin
- Michael Hull
- Alessandro Sisto
- Yves Cornulier
In Geometry and Topology
- Anthony Genevois
- Carolyn R. Abbott
- S. Balasubramanya
- Alexandre Martin
- Denis V. Osin
- Hung Cong Tran
- Alessandro Sisto
- Ashot Minasyan
Citations in the corpus
- Hyperbolic structures on groups (2017, background): “ing d(x;y) R, we have #fg2Gjd(x;gx) ";d(y;gy) "gN: Groups acting acylindrically on hyperbolic spaces have received a lot of attention in the recent years. For a brief survey we refer to [64]. The goal of our paper is to initiate the study of the posets H(G) and AH(G) for various groups Gan”
- Automorphisms of graph products of groups from a geometric perspective (2018, background): “The first property we investigate is the notion of acylindrical hyperbolicity introduced by Osin in [39], which unifies several known classes of groups with ‘negatively curved’ features such as relatively hyperbolic groups and mapping class groups (we refer to [40] for more information).”