Volume 21, issue 1 (2021)

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

Volume 21
Issue 2, 543–1074
Issue 1, 1–541

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
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Reflection trees of graphs as boundaries of Coxeter groups

Jacek Świątkowski

Algebraic & Geometric Topology 21 (2021) 351–420
Abstract

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.

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