Hyperbolic groups and local connectivity
Group Theory
2024-01-15 v2 Geometric Topology
Abstract
The goal of this paper is to give an exposition of some results of Bestvina-Mess on local connectivity of the boundary of a one-ended word hyperbolic group. We also give elementary proofs that all hyperbolic groups are semistable at infinity and their boundaries are linearly connected in the one-ended case. Geoghegan first observed that semistability at infinity is a consequence of local connectivity using ideas from shape theory, and Bonk-Kleiner proved linear connectivity using analytical methods. The methods in this paper are closely based on the original ideas of Bestvina-Mess.
Keywords
Cite
@article{arxiv.2308.14964,
title = {Hyperbolic groups and local connectivity},
author = {G. Christopher Hruska and Kim Ruane},
journal= {arXiv preprint arXiv:2308.14964},
year = {2024}
}
Comments
Dedicated to Mike Mihalik on his 70th birthday. 16 pages. Version 2 includes minor revisions based on referee feedback