a1 Department of Mathematics, University of Toronto, 40 St. George Street, Room 6092, Toronto, Ontario, Canada (email: email@example.com)
We prove that if G is a countable discrete group with property (T) over an infinite subgroup H≤G which contains an infinite Abelian subgroup or is normal, then G has continuum-many orbit-inequivalent measure-preserving almost-everywhere-free ergodic actions on a standard Borel probability space. Further, we obtain that the measure-preserving almost-everywhere-free ergodic actions of such a G cannot be classified up to orbit equivalence by a reasonable assignment of countable structures as complete invariants. We also obtain a strengthening and a new proof of a non-classification result of Foreman and Weiss for conjugacy of measure-preserving ergodic almost-everywhere-free actions of discrete countable groups.
(Received February 26 2007)
(Revised April 14 2008)