# Orbit inequivalent actions of non-amenable groups

#### by Inessa Epstein

Institution: University of California, Los Angeles
Date: Wed 2nd May 2007
Time: 4:30 PM
Location: Room 107, Richard Berry Building

Abstract: We consider a Borel action of a countable group G on a standard Borel space X with a probability measure such that the action is free, ergodic and measure preserving. We may think of two such actions on spaces X and Y as being orbit equivalent if there is a Borel map witnessing that the actions are the same up to null sets. It is known that an amenable group admits only one free, ergodic, measure preserving Borel action up to
orbit equivalence. We show that a non-amenable group admits continuum many orbit inequivalent of this type.