Instability for rank one factors of product actions

TL;DR

This paper challenges a common interpretation of the Katok-Spatzier conjecture by providing a counterexample and proposing alternative questions for future research.

Contribution

It introduces a counterexample to a standard interpretation of the Katok-Spatzier conjecture and suggests new questions for the field.

Findings

Counterexample to a standard interpretation of the conjecture

Raises new questions for further investigation

Challenges existing assumptions in the field

Abstract

We provide a counterexample to a standard interpretation of the Katok-Spatzier conjecture, and pose questions which may serve as reasonable replacements.