Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part I: The dynamically coherent case
Dynamical Systems
2022-03-18 v4 Geometric Topology
Abstract
We study 3-dimensional dynamically coherent partially hyperbolic diffeomorphisms that are homotopic to the identity, focusing on the transverse geometry and topology of the center stable and center unstable foliations, and the dynamics within their leaves. We find a structural dichotomy for these foliations, which we use to show that every such diffeomorphism on a hyperbolic or Seifert fibered 3-manifold is leaf conjugate to the time one map of a (topological) Anosov flow. This proves a classification conjecture of Hertz-Hertz-Ures in hyperbolic 3-manifolds and in the homotopy class of the identity of Seifert manifolds.
Keywords
Cite
@article{arxiv.1908.06227,
title = {Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part I: The dynamically coherent case},
author = {Thomas Barthelmé and Sergio R. Fenley and Steven Frankel and Rafael Potrie},
journal= {arXiv preprint arXiv:1908.06227},
year = {2022}
}
Comments
v4: Final accepted version. Some improvement in the text thanks to referees