Title: Infinite generation of non-cocompact lattices on right-angled buildings
Abstract: Let Gamma be a non-cocompact lattice on a right-angled building X. Examples of such X include products of trees, or Bourdon’s building I_p,q, which has apartments hyperbolic planes tesselated by right-angled p-gons and all vertex links the complete bipartite graph K_q,q. We prove that if Gamma has a strict fundamental domain then Gamma is not finitely generated. The proof uses a topological criterion for finite generation and the separation properties of subcomplexes of X called tree-walls. This is joint work with Kevin Wortman (Utah).