Mykyta Vieprik

Classification of rank-one actions via the cutting-and-stacking parameters

Let G be a discrete countable infinite group. Let T and T' be two rank-one
σ-finite measure preserving actions of G and let S and S' be the cutting-and-
stacking parameters that determine T and T' respectively. We find necessary
and sufficient conditions on S and S' under which T and T' are isomorphic.
We also show that the isomorphism equivalence relation is a Gδ -subset in
the Cartesian square of the set of all admissible parameters endowed with
the natural Polish topology.
During the talk, we will introduce rank-one transformations and (C,F)-
constructions, review previous results on the isomorphism problem for rank-
one transformations, and present the main result along with the main idea
of the proof.
This talk is based on joint work with Alexandre Danilenko.