Speaker: Professor Valentin Ya. Golodets, UNSW

Place: Red Centre, room 4082.
Date: the 6th of September.
Time: 12:00 -- 13:00.

Abstract:


The cost of an equivalence relation is an important numerical invariant in
ergodic theory introduced recently by H.Levitt. It allowed to discover some
new properties of Borel actions of non-amenable countable groups preserving
a finite measure. A theory of the costs were developed recently by Gaboriau,
Hjorth, Kechris, Miller and other authors.

To prove this equality we develop some results of the cost theory. We also use
index cocycles of Feldman, Sutherland and Zimmer.

This result has some applications. In particulary , we can prove that F is
amenable if and only if E is amenable.

This research was done in cooperation with Tony Dooley.