Seifert manifolds admitting partially hyperbolic diffeomorphisms

TL;DR

This paper characterizes 3D Seifert manifolds that support transitive partially hyperbolic diffeomorphisms, linking their existence to the presence of Anosov flows in certain circle bundles over higher-genus surfaces.

Contribution

It provides a complete characterization of which Seifert manifolds admit these diffeomorphisms, establishing a connection with Anosov flows.

Findings

Circle bundles over higher-genus surfaces admit transitive partially hyperbolic diffeomorphisms iff they admit Anosov flows.

Characterization of Seifert manifolds supporting such diffeomorphisms.

Link between dynamical properties and topological structure of manifolds.

Abstract

We characterize which 3-dimensional Seifert manifolds admit transitive partially hyperbolic diffeomorphisms. In particular, a circle bundle over a higher-genus surface admits a transitive partially hyperbolic diffeomorphism if and only if it admits an Anosov flow.