Continuous cocycle superrigidity for coinduced actions and relative ends

TL;DR

This paper establishes that specific coinduced group actions are continuously cocycle superrigid under certain subgroup conditions, highlighting the importance of the relative end assumption for this property.

Contribution

It proves continuous cocycle superrigidity for coinduced actions with finitely generated commensurated subgroups having one relative end, and demonstrates the necessity of the relative end condition.

Findings

Coinduced actions are superrigid under the specified conditions.

The relative end assumption is shown to be necessary for superrigidity.

The work extends understanding of cocycle superrigidity in group actions.

Abstract

We prove that certain coinduced actions for an inclusion of finitely generated commensurated subgroups with relative one end are continuous cocycle superrigid actions. We also show the necessity for the relative end assumption.