Infinite Generaton of Non-Cocompact Lattices on Right-Angled Buildings

SPECIAL LECTURE
Topic:Infinite Generaton of Non-Cocompact Lattices on Right-Angled Buildings
Speaker:Anne Thomas
Affiliation:University of Sydney, NSW
Date:Wednesday, April 6
Time/Room:4:00pm - 5:00pm/S-101
Video Link:https://video.ias.edu/special-lecture/thomas

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).