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2009 A smallest irreducible lattice in the product of trees
David Janzen, Daniel T Wise
Algebr. Geom. Topol. 9(4): 2191-2201 (2009). DOI: 10.2140/agt.2009.9.2191

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.

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David Janzen. Daniel T Wise. "A smallest irreducible lattice in the product of trees." Algebr. Geom. Topol. 9 (4) 2191 - 2201, 2009. https://doi.org/10.2140/agt.2009.9.2191

Information

Received: 4 April 2007; Revised: 9 March 2009; Accepted: 26 August 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1220.20039
MathSciNet: MR2558308
Digital Object Identifier: 10.2140/agt.2009.9.2191

Subjects:
Primary: 20F67

Rights: Copyright © 2009 Mathematical Sciences Publishers

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