Partially hyperbolic diffeomorphisms homotopic to the identity on 3-manifolds

TL;DR

This paper discusses progress in classifying partially hyperbolic diffeomorphisms on 3-manifolds, especially focusing on the case of dynamically coherent diffeomorphisms, with detailed proofs to follow.

Contribution

It provides initial results and an outline for classifying partially hyperbolic diffeomorphisms homotopic to the identity on 3-manifolds, emphasizing the dynamically coherent case.

Findings

Initial classification results presented

Outline of proof strategies provided

Focus on dynamically coherent diffeomorphisms

Abstract

We announce some results towards the classification of partially hyperbolic diffeomorphisms on 3-manifolds, and outline the proofs in the case when the diffeomorphism is dynamically coherent. Detailed proofs are long and technical and will appear later.