Global rigidity of higher rank Anosov algebraic actions

TL;DR

This paper proves that smooth Anosov actions of Z^r on tori and nilmanifolds are conjugate to automorphism actions, provided they lack rank-one factors, extending understanding of rigidity in higher rank dynamics.

Contribution

It establishes a global rigidity result for higher rank Anosov Z^r-actions on tori and nilmanifolds, showing they are smoothly conjugate to algebraic automorphisms.

Findings

All smooth Anosov Z^r-actions without rank-one factors are conjugate to automorphisms.

The result applies to actions on tori and nilmanifolds.

It excludes actions with rank-one factor actions.

Abstract

We show that all $C^\infty$ Anosov $Z^r$-actions on tori and nilmanifolds without rank-one factor actions are, up to $C^\infty$ conjugacy, actions by automorphisms.