AF-equivalence relations and their cocycles

Details AF-equivalence relations and their cocycles AF-equivalence relations and their cocycles

2001-11-15

arxiv.org/abs/math/0111182v1

Mathematics

Operator Algebras

15 pages, talk at 4th International Conference on Operator Algebras, July 2-7 2001, Constanza, Romania

Scientific paper

After a review of some of the main results about hyperfinite equivalence relations and their cocycles in the measured setting, we give a definition of a topological AF-equivalence relation. We show that every cocycle is cohomologous to a quasi-product cocycle. We then study the problem of determining the quasi-invariant probability measures admitting a given cocycle as their Radon-Nikodym derivative.

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