Hyperbolic groups and local connectivity

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Bibliographic Details
Main Authors:	Hruska, G. Christopher, Ruane, Kim
Format:	Preprint
Published:	2023
Subjects:	Group Theory Geometric Topology 20F67, 57M07
Online Access:	Acceder al recurso
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author	Hruska, G. Christopher Ruane, Kim
author_facet	Hruska, G. Christopher Ruane, Kim
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2308_14964
institution	arXiv
publishDate	2023
record_format	arxiv
spellingShingle	Hyperbolic groups and local connectivity Hruska, G. Christopher Ruane, Kim Group Theory Geometric Topology 20F67, 57M07 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.
title	Hyperbolic groups and local connectivity
topic	Group Theory Geometric Topology 20F67, 57M07
url	https://arxiv.org/abs/2308.14964

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