Volume 22, issue 2 (2022)

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

Volume 22
Issue 3, 991–1495
Issue 2, 473–990
Issue 1, 1–472

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
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
Leighton's theorem: Extensions, limitations and quasitrees

Martin R Bridson and Sam Shepherd

Algebraic & Geometric Topology 22 (2022) 881–917
Abstract

Leighton’s theorem states that if there is a tree T that covers two finite graphs G1 and G2, then there is a finite graph Ĝ that is covered by T and covers both G1 and G2. We prove that this result does not extend to regular covers by graphs other than trees. Nor does it extend to nonregular covers by a quasitree, even if the automorphism group of the quasitree contains a uniform lattice. But it does extend to regular coverings by quasitrees.

Keywords
quasitrees, covering spaces, Leighton's theorem
Mathematical Subject Classification
Primary: 05C25, 20F65, 20F67
References
Publication
Received: 9 September 2020
Revised: 13 January 2021
Accepted: 1 February 2021
Published: 3 August 2022
Authors
Martin R Bridson
Mathematical Institute
University of Oxford
Oxford
United Kingdom
Sam Shepherd
Department of Mathematics
Vanderbilt University
Nashville, TN
United States