Anne Thomas (University of Chicago)

Friday 25th August, 12.05-12.55pm, Carslaw 373

Lattices in automorphism groups of polyhedral complexes

Let G be a locally compact topological group with Haar measure mu. A discrete subgroup Gamma of G is a lattice if its covolume mu(Gamma\G) is finite. The classical context for studying lattices is when G is a semisimple Lie group. We consider lattices in automorphism groups of locally finite polyhedral complexes. Examples include non-classical buildings, and complexes whose links are graphs such as the Petersen graph. We study covolumes, construct infinite ascending sequences of lattices, and (in joint work with Seonhee Lim) obtain some bounds on the number of "overlattices" of a given lattice Gamma.