Year: 2015
Type: preprint
Abstract: 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 $n\geq 2$. 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 Dunwoody's example of an inaccessible group as a counterexample.
Source: arXiv (Cornell University)
Author: Abbott, Carolyn R.
Institution: University of Wisconsin–Madison
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951618272