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

Volume 25, 1 issue

Volume 24, 9 issues

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
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
A cubulation with no factor system

Sam Shepherd
Algebraic & Geometric Topology 25 (2025) 255–266
DOI: 10.2140/agt.2025.25.255
Abstract

The primary method for showing that a given cubulated group is hierarchically hyperbolic is by constructing a factor system on the cube complex. We show that such a construction is not always possible, namely we construct a cubulated group for which the cube complex does not have a factor system. We also construct a cubulated group for which the induced action on the contact graph is not acylindrical.

Keywords
CAT(0) cube complex, cubulated group, factor system, contact graph, acylindrical
Mathematical Subject Classification
Primary: 20F65
Secondary: 20F67
References
Publication
Received: 27 February 2023
Revised: 13 June 2023
Accepted: 9 September 2023
Published: 5 March 2025
Authors
Sam Shepherd
Institut für Mathematische Logik und Grundlagenforschung
Fachbereich Mathematik und Informatik
Universität Münster
Münster
Germany
© 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

Open Access made possible by participating institutions via Subscribe to Open.