## University of Sydney Algebra Seminar

# Anne Thomas (University of Sydney)

## Friday 8th October, 12.05-12.55pm, Carslaw 175

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

Let Gamma be a non-cocompact lattice on a locally finite regular right-angled building X. Examples of such X include products of locally finite regular or biregular 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).