**SMS scnews item created by James East at Wed 6 Oct 2010 0950**

Type: Seminar

Distribution: World

Expiry: 8 Oct 2010

**Calendar1: 8 Oct 2010 1205-1255**

**CalLoc1: Carslaw 175**

Auth: jamese@bari.maths.usyd.edu.au

### Algebra Seminar

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

### Anne Thomas

#### Friday October 8, 12:05--12:55pm, Carslaw 175

###### Abstract

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).

---------------------------------------------------------------------------------------

After the seminar we will take the speaker to lunch.

See the Algebra Seminar web page for information about other seminars in the series.

James East james.east@sydney.edu.au