Acylindrical hyperbolicity of groups acting on trees
By Ashot Minasyan, Denis V. Osin. Mathematische Annalen, 2013
170 citations recorded by the source corpus.
We provide new examples of acylindrically hyperbolic groups arising from actions on simplicial trees. In particular, we consider amalgamated products and HNN-extensions, one-relator groups, automorphism groups of polynomial algebras, 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3$$\end{document}-manifold groups and graph products. Acylindrical hyperbolicity is then used to obtain some results about the algebraic structure, analytic properties and measure equivalence rigidity of groups from these classes.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b02ee11ea162df0af408b6a056d0cf2301b84e11
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
- Anthony Genevois
- Alessandro Sisto
- Carolyn R. Abbott
- Dominik Gruber
- Denis V. Osin
- S. Balasubramanya
- Hung Cong Tran
- Jason A. Behrstock
In Mathematical Physics
- Anthony Genevois
- Alessandro Sisto
- Carolyn R. Abbott
- Denis V. Osin
- Dominik Gruber
- S. Balasubramanya
- Hung Cong Tran
- Mark F. Hagen
Citations in the corpus
- Hyperbolicities in CAT(0) cube complexes (2017, methodology): “19 is applied to the action on the corresponding Bass-Serre tree in [MO15].”
- Infinitely presented graphical small cancellation groups are acylindrically hyperbolic (2014, background): “The class of acylindrically hyperbolic groups is extensive: It contains all non-elementary hyperbolic and relatively hyperbolic groups, mapping class groups, Out(Fn), the Cremona group in dimension 2, many CAT(0) groups and many groups acting on trees, see [17, 35] and references therein.”
- GROUPS ACTING ACYLINDRICALLY ON HYPERBOLIC SPACES (2017, methodology): “here Kim and Koberda construct explicitly acylindrical actions of right angled Artin groups. A similar theorem holds for graph products of groups and, even more generally, subgroups of graph products [47]. For a survey of examples of acylindrically hyperbolic groups arising from actions on CAT(0) cu”
- Hyperbolic structures on groups (2017, background): “ually cyclic groups acting properly on proper CAT(0) spaces and containing a rank one isometry, most 3-manifold groups, groups of deciency at least 2 and many other examples. For details we refer to [27,52,62,63] and references therein. 2.2. Induced hyperbolic structures. The proof of the second sta”