Aspherical products which do not support Anosov diffeomorphisms

TL;DR

This paper proves that certain aspherical product manifolds, including products of nilmanifolds and negatively curved manifolds, cannot support Anosov diffeomorphisms, extending understanding of dynamical systems on complex manifolds.

Contribution

It establishes new non-existence results for Anosov diffeomorphisms on specific classes of aspherical product manifolds.

Findings

Products of infranilmanifolds and certain aspherical manifolds do not support Anosov diffeomorphisms.

Products of nilmanifolds and negatively curved manifolds of dimension ≥ 3 lack Anosov diffeomorphisms.

The results extend previous non-existence theorems to broader classes of manifolds.

Abstract

We show that the product of infranilmanifolds with certain aspherical closed manifolds do not support Anosov diffeomorphisms. As a special case, we obtain that products of a nilmanifold and negatively curved manifolds of dimension at least 3 do not support Anosov diffeomorphisms.