Infinite generation of non-cocompact lattices on right-angled buildings

Anne Thomas and Kevin Wortman

Abstract

Let \(\Gamma\) be a non-cocompact lattice on a locally finite regular right-angled building \(X\). We prove that if \(\Gamma\) has a strict fundamental domain then \(\Gamma\) is not finitely generated. We use the separation properties of subcomplexes of \(X\) called tree-walls.