Volume 9, issue 4 (2009)

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

Volume 19
Issue 6, 2677–3215
Issue 5, 2151–2676
Issue 4, 1619–2150
Issue 3, 1079–1618
Issue 2, 533–1078
Issue 1, 1–532

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

Author Index
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
To Appear
 
Other MSP Journals
A smallest irreducible lattice in the product of trees

David Janzen and Daniel T Wise

Algebraic & Geometric Topology 9 (2009) 2191–2201
Abstract

We produce a nonpositively curved square complex X containing exactly four squares. Its universal cover X̃T4 × T4 is isomorphic to the product of two 4–valent trees. The group π1X is a lattice in Aut(X̃) but π1X is not virtually a nontrivial product of free groups. There is no such example with fewer than four squares. The main ingredient in our analysis is that X̃ contains an “anti-torus” which is a certain aperiodically tiled plane.

Keywords
irreducible lattice, CAT(0) cube complex
Mathematical Subject Classification 2000
Primary: 20F67
References
Publication
Received: 4 April 2007
Revised: 9 March 2009
Accepted: 26 August 2009
Published: 27 October 2009
Authors
David Janzen
Math & Stats
McGill University
Montreal, Quebec H3A 2K6
Canada
Daniel T Wise
Math & Stats
McGill University
Montreal, Quebec H3A 2K6
Canada
http://www.math.mcgill.ca/wise