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

Abstract

Let Γbe a non-cocompact lattice on a locally finite regular right-angled building X. We prove that if Γhas a strict fundamental domain then Γis not finitely generated. We use the separation properties of subcomplexes of X called tree-walls.

11 pages, one figure. v2: new example and references in the introduction. To appear in Algebr. Geom. Top