Geometry, Topology and Dynamics Seminar
Ana Rechtman
Ecole Normale Superieure de Lyon
A Følner foliation that is not amenable
Abstract: In this talk I will define what an amenable foliation is and the relation with the property of
having Følner leaves. Amenability is defined with respect to a transverse invariant measure.
Using a plug, we will construct a non amenable smooth (or even real analytic) foliation of a
compact manifold whose leaves are Følner, which has the nice property of having a transverse
invariant volume. This is a counter-example to R. Brooks statement (from 1983): a foliation
having almost all its leaves Følner is amenable, with respect to a transverse invariant measure.
In 2001, V. A. Kaimanovich had constructed a counter-example to this statement, with the
inconvenience that the transverse invariant measure was not locally finite.
A foliation whose leaves are Følner is amenable if all the leaves are dense. I will explain
the main ideas of the proof of this last statement.
Wednesday November 12, 2008 at 3:00 PM in SEO 612