ﻻ يوجد ملخص باللغة العربية
The class of acylindrically hyperbolic groups, which are groups that admit a certain type of non-elementary action on a hyperbolic space, contains many interesting groups such as non-exceptional mapping class groups and $operatorname{Out}(mathbb F_n)$ for $ngeq 2$. In such a group, a generalized loxodromic element is one that is loxodromic for some acylindrical action of the group on a hyperbolic space. Osin asks whether every finitely generated group has an acylindrical action on a hyperbolic space for which all generalized loxodromic elements are loxodromic. We answer this question in the negative, using Dunwoodys example of an inaccessible group as a counterexample.
We consider two manifestations of non-positive curvature: acylindrical actions on hyperbolic spaces and quasigeodesic stability. We study these properties for the class of hierarchically hyperbolic groups, which is a general framework for studying ma
We simplify the construction of projection complexes due to Bestvina-Bromberg-Fujiwara. To do so, we introduce a sharper version of the Behrstock inequality, and show that it can always be enforced. Furthermore, we use the new setup to prove acylindr
A Kleinian group $Gamma < mathrm{Isom}(mathbb H^3)$ is called convex cocompact if any orbit of $Gamma$ in $mathbb H^3$ is quasiconvex or, equivalently, $Gamma$ acts cocompactly on the convex hull of its limit set in $partial mathbb H^3$. Subgroup sta
We provide new examples of acylindrically hyperbolic groups arising from actions on simplicial trees. In particular, we consider amalgamated products and HNN-extensions, 1-relator groups, automorphism groups of polynomial algebras, 3-manifold groups
We study completions of the group algebra of a finitely generated group and relate nuclearity of such a completion to growth properties of the group. This extends previous work of Jolissaint on nuclearity of rapidly decreasing functions on a finitely