Lattices acting on right-angled buildings

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.