Volume 20, issue 3 (2020)

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

Volume 20
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

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
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Roller boundaries for median spaces and algebras

Elia Fioravanti

Algebraic & Geometric Topology 20 (2020) 1325–1370
Abstract

We construct compactifications for median spaces with compact intervals, generalising Roller boundaries of CAT(0) cube complexes. Examples of median spaces with compact intervals include all finite-rank median spaces and all proper median spaces of infinite rank. Our methods also apply to general median algebras, where we recover the zero-completions of Bandelt and Meletiou (1993). Along the way, we prove various properties of halfspaces in finite-rank median spaces and a duality result for locally convex median spaces.

Keywords
median space, median algebra, horofunction compactification, Roller boundary, spaces with walls
Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 20F67, 22F50, 51F99, 57M99
References
Publication
Received: 25 August 2018
Revised: 24 May 2019
Accepted: 26 August 2019
Published: 27 May 2020
Authors
Elia Fioravanti
Mathematical Institute
University of Oxford
Oxford
United Kingdom