Volume 6, issue 3 (2006)

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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 $Aut\left(X\right)$ share many properties with tree lattices. For example, we characterise the set of covolumes of uniform and of nonuniform lattices in $Aut\left(X\right)$, and show that the group $Aut\left(X\right)$ 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
Primary: 22D05
Secondary: 20E42
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