Volume 24, issue 2 (2020)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 3, 1075–1614
Issue 2, 533–1073
Issue 1, 1–532

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Trees of manifolds as boundaries of spaces and groups

Jacek Świątkowski

Geometry & Topology 24 (2020) 593–622
Abstract

We show that trees of manifolds, the topological spaces introduced by Jakobsche, appear as boundaries at infinity of various spaces and groups. In particular, they appear as Gromov boundaries of some hyperbolic groups, of arbitrary dimension, obtained by the procedure of strict hyperbolization. We also recognize these spaces as boundaries of arbitrary Coxeter groups with manifold nerves and as Gromov boundaries of the fundamental groups of singular spaces obtained from some finite-volume hyperbolic manifolds by cutting off their cusps and collapsing the resulting boundary tori to points.

Keywords
hyperbolic group, Gromov boundary
Mathematical Subject Classification 2010
Primary: 20F67
Secondary: 20F65, 57M07
References
Publication
Received: 25 April 2013
Revised: 19 January 2016
Accepted: 6 August 2019
Published: 23 September 2020
Proposed: Steve Ferry
Seconded: John Lott, Bruce Kleiner
Authors
Jacek Świątkowski
Instytut Matematyczny
Uniwersytet Wrocławski
Wrocław
Poland