# Gaboriau's work on the theory of cost, I

*Algebra/Geometry/Topology Seminar*

*by Greg Hjorth*

*Institution:*Melbourne/UCLA

*Date: Thu 19th February 2009*

*Time: 2:30 PM*

*Location: Room 213*

*Abstract*: The cost of an equivalence relation is a numerical invariant which is defined in the context of an orbit equivalence relation arising from a measure preserving action of a countable group on a standard Borel measure space. Although the notion was first defined by Levitt, it was not until the breakthrough work of Gaboriau that it was possible to calculate the cost in non-trivial cases.

I intend to describe Gaboriau's theorem on the cost of treeable equivalence relations, open problems in the area, and how the theory of cost has a surprising connection with a long standing open problem in low dimensional topology.

*For More Information:* S.Tillmann@ms.unimelb.edu.au