Volume 6, issue 3 (2006)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Lattices acting on right-angled buildings

Anne Thomas

Algebraic & Geometric Topology 6 (2006) 1215–1238

arXiv: math.GR/0508385

Abstract

Let X be a right-angled building. We show that the lattices in Aut(X) share many properties with tree lattices. For example, we characterise the set of covolumes of uniform and of nonuniform lattices in Aut(X), and show that the group Aut(X) admits an infinite ascending tower of uniform and of nonuniform lattices. These results are proved by constructing a functor from graphs of groups to complexes of groups.

Keywords
lattice, polyhedral complex, right-angled building
Mathematical Subject Classification 2000
Primary: 22D05
Secondary: 20E42
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Publication
Received: 3 March 2006
Revised: 29 June 2006
Accepted: 30 June 2006
Published: 7 September 2006
Authors
Anne Thomas
Department of Mathematics
University of Chicago
5734 South University Ave
Chicago IL 60637
USA