Continuous cocycle superrigidity for the full shift over a finitely generated torsion group

TL;DR

This paper extends continuous cocycle superrigidity results to all one-ended groups, removing previous restrictions requiring an infinite order element, thus broadening the class of groups for which such rigidity holds.

Contribution

It proves that continuous cocycle superrigidity applies to all one-ended groups, not just those with an infinite order element, generalizing prior results.

Findings

Superrigidity holds for all one-ended groups.

The hypothesis of having an infinite order element is unnecessary.

The result applies to the full shift over these groups.

Abstract

Chung and Jiang showed that, if a one ended group contains an infinite order element, then every continuous cocycle over the full shift on that group, taking values in a discrete group, must be cohomologous to a homomorphism. We show that their conclusion holds for all one ended groups, so that the hypothesis of admitting an infinite order element may be omitted.