Geometry, Topology and Dynamics Seminar
Inessa Epstein
Caltech
Measurable subgroups and orbit inequivalent actions
Abstract: We consider a countable group G acting in a Borel way by measure preserving automorphisms on a standard probability space X.
The orbits of this action give rise to an equivalence relation on X.
We say two measure preserving actions of groups G and H on spaces X and Y, respectively, are orbit equivalent if there is a measure preserving
bijection between conull subsets of X and Y identifying the orbits.
The work of Hjorth, Gaboriau, Popa and Ioana has established that every group containing a copy of the free group on two generators admits continuum many orbit
inequivalent actions that are free, measure preserving and ergodic.
Gaboriau and Lyons, notably using a theorem of Pak and Smirnova-Nagnibeda, proved that every non-amenable group admits the free group on two generators as a measured subgroup.
We discuss a result that every non-amenable group admits continuum many orbit inequivalent free, measure preserving, ergodic actions.
Wednesday August 27, 2008 at 3:00 PM in SEO 612