Lattices acting on right-angled buildings

Thomas, Anne

doi:10.2140/agt.2006.6.1215

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Lattices acting on right-angled buildings

Anne Thomas

Algebraic & Geometric Topology 6 (2006) 1215–1238

DOI: 10.2140/agt.2006.6.1215

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

Volume 6, issue 3 (2006)