Cross-sections of Borel flows

Speaker: Kostya Slutsky, University of Copenhagen.

Questions about measure-preserving flows can frequently be reduced to the corresponding problems for a single transformation by finding an appropriate countable cross-section.  And it is sometimes desirable to find a cross-section with special restrictions on distances between its points.  In the context of ergodic theory it was shown by Rudolph that one can always find a cross-section with only two possible distances between neighbouring points.  The main result of the talk is a similar result in a purely Borel context: every free Borel flow on a standard Borel space admits a cross-section with only two possible distances.  We shall also discuss some applications to orbit equivalences of flows.