turkmath.org

In this talk, we analyze the complexity of the topological conjugacy relation on Cantor minimal systems from the point of view of descriptive set theory. We shall show that topological conjugacy of pointed Cantor minimal systems is Borel bireducible with the equality of countable sets of reals. We will also show that this is a lower bound for the Borel complexity of topological conjugacy of Cantor minimal systems. If time permits, we will cover some applications of our results to properly ordered Bratteli diagrams.