Title: | Gaboriau's work on the theory of cost |
Speaker: | Greg Hjorth (Melbourne/UCLA) |
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. |