Classification of partially hyperbolic diffeomorphisms in 3-manifolds with solvable fundamental group

TL;DR

This paper classifies partially hyperbolic diffeomorphisms on 3-manifolds with solvable fundamental group, showing they are dynamically coherent and leaf conjugate to algebraic models unless they admit certain tori.

Contribution

It provides a complete classification of such diffeomorphisms, confirming conjectures in the case of solvable fundamental groups and identifying conditions for algebraic conjugacy.

Findings

Diffeomorphisms without attracting or repelling tori are dynamically coherent.

Such diffeomorphisms are leaf conjugate to known algebraic examples.

The classification includes manifolds supporting Anosov flows.

Abstract

A classification of partially hyperbolic diffeomorphisms on 3-dimensional manifolds with (virtually) solvable fundamental group is obtained. If such a diffeomorphism does not admit a periodic attracting or repelling two-dimensional torus, it is dynamically coherent and leaf conjugate to a known algebraic example. This classification includes manifolds which support Anosov flows, and it confirms conjectures by Rodriguez Hertz--Rodriguez Hertz--Ures and Pujals in the specific case of solvable fundamental group.