Volume 21, issue 1 (2021)

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

Volume 24
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Reflection trees of graphs as boundaries of Coxeter groups

Jacek Świątkowski

Algebraic & Geometric Topology 21 (2021) 351–420

To any finite graph X (viewed as a topological space) we associate an explicit compact metric space 𝒳r(X), which we call the reflection tree of graphs X. This space is of topological dimension 1 and its connected components are locally connected. We show that if X is appropriately triangulated (as a simplicial graph Γ for which X is the geometric realization) then the visual boundary (W,S) of the right-angled Coxeter system (W,S) with the nerve isomorphic to Γ is homeomorphic to 𝒳r(X). For each X, this yields in particular many word hyperbolic groups with Gromov boundary homeomorphic to the space 𝒳r(X).

I dedicate this paper to the memory of my parents.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Coxeter group, visual boundary, hyperbolic group, Gromov boundary
Mathematical Subject Classification 2010
Primary: 20F65, 20F67
Secondary: 20F55, 57M07
Received: 27 August 2019
Accepted: 15 June 2020
Published: 25 February 2021
Jacek Świątkowski
Instytut Matematyczny
Uniwersytet Wrocławski