Geometry, Topology and Dynamics Seminar
Darren Creutz
UCLA
Normal Subgroup and Factor Theorems for Commensurators
Abstract: We present a Normal Subgroup Theorem for (dense) commensurators of
lattices in arbitrary locally compact groups (not necessarily Lie).
In particular, any normal subgroup of a (dense) commensurator of an
(integrable) lattice in a simple topological group necessarily
contains (up to finite index) the lattice.
The approach, as in Margulis' Normal Subgroup Theorem, involves, on
the one hand, using cohomology and rigidity theory to prove a certain
group has property (T), and on the other hand, Furstenberg's Boundary
Theory to prove this group is also amenable. We will focus more on the
amenability half of the proof, in particular our new "Factor Theorem"
which facilitates the proof (and which is of independent interest).
Monday November 8, 2010 at 3:00 PM in SEO 636