Orbit equivalence superrigidity for type III${}_0$ actions

Abstract

We prove the first orbit equivalence superrigidity results for actions of type III${}_{\lambda }$ when $\lambda \ne 1$. These actions arise as skew products of actions of dense subgroups of $SL(n,\mathbb{R})$ on the sphere $S^{n-1}$ and they can have any prescribed associated flow.

v2: minor changes, final version, to appear in Ergodic Theory and Dynamical Systems

References in corpus (3)

• Cocycle superrigidity for profinite actions of irreducible lattices
• Non-ergodic actions, cocycles and superrigidity
• Superrigidity for dense subgroups of Lie groups and their actions on homogeneous spaces