Approximate equivalence of actions
arXiv:1511.00307
Abstract
We consider several weaker versions of the notion of conjugacy and orbit equivalence of measure preserving actions of countable groups on probability spaces, involving equivalence of the ultrapower actions and asymptotic intertwining conditions. We compare them with the other existing equivalence relations between group actions, and study the usual type of rigidity questions around these new concepts (superrigidity, calculation of invariants, etc).
45 pages; minor errors fixed, remark 4.10.2 added; paper will appear in this form in Ergodic Theory and Dynamical Systems