Totally non-symplectic Anosov actions on tori and nilmanifolds

TL;DR

This paper proves that certain complex dynamical systems called totally non-symplectic Anosov actions on tori and nilmanifolds are smoothly equivalent to simpler affine actions, under irreducibility conditions.

Contribution

It establishes a smooth conjugacy between irreducible totally non-symplectic Anosov actions and affine actions on tori and nilmanifolds, extending understanding of their structure.

Findings

Sufficient conditions for smooth conjugacy to affine actions

Classification of Anosov actions on tori and nilmanifolds

Extension of rigidity results in higher rank abelian group actions

Abstract

We show that sufficiently irreducible totally non-symplectic Anosov actions of higher rank abelian groups on tori and nilmanifolds are smoothly conjugate to affine actions.