# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1706.03743