Geometry, Topology and Dynamics Seminar
Yair Glasner
Ben Gurion University, and University of Utah
Invariant random subgroups of linear groups.
Abstract: An invariant random subgroup (IRS for short) of a countable group G is a conjugation invariant probability measure on the (compact metric) space of all subgroups of G.
Theorem:
Let G < \GL_n(F) be a countable non-amenable linear group with a simple center free Zariski closure. Then.
There is a topology on G such that for every IRS, almost every non-trivial subgroup of G is open.
G contains a dense free subgroup F in this topology.
For every IRS, the map taking a subgroup H < G to its intersection with F becomes an F-invariant isomorphism of probability spaces.
We say that an action of a group G on a probability space is a.s.n.f if almost all point stabilizers are non-trivial.
Corollary:
Let G as above acts on two probability spaces X and Y. If both actions are a.s.n.f then so is the diagonal action on the product.
Monday March 10, 2014 at 3:00 PM in SEO 636