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

Primary: 22D05

Secondary: 20E42

References

Publication

Received: 3 March 2006
Revised: 29 June 2006
Accepted: 30 June 2006
Published: 7 September 2006

Authors