Continuous orbit equivalence rigidity for left-right wreath product actions

TL;DR

This paper extends orbit equivalence superrigidity results from measurable to topological settings for certain group actions, demonstrating that some actions are uniquely determined by their orbit structure in a continuous framework.

Contribution

It establishes topological orbit equivalence superrigidity for left-right wreath product actions, extending previous measurable results to the continuous setting.

Findings

Proves continuous cocycle superrigidity for generalized full shifts.

Identifies minimal, topologically free actions that are superrigid.

Extends superrigidity results to a broader topological context.

Abstract

Drimbe and Vaes proved an orbit equivalence superrigidity theorem for left-right wreath product actions in the measurable setting. We establish the counterpart result in the topological setting for continuous orbit equivalence. This gives us minimal, topologically free actions that are continuous orbit equivalence superrigid. One main ingredient for the proof is to show continuous cocycle superrigidity for certain generalized full shifts, extending our previous result with Chung.