Partially hyperbolic diffeomorphisms with compact center foliations
Dynamical Systems
2012-01-18 v2 Geometric Topology
Abstract
Let f:M->M be a partially hyperbolic diffeomorphism such that all of its center leaves are compact. We prove that Sullivan's example of a circle foliation that has arbitrary long leaves cannot be the center foliation of f. This is proved by thorough study of the accessible boundaries of the center-stable and the center-unstable leaves. Also we show that a finite cover of f fibers over an Anosov toral automorphism if one of the following conditions is met: 1. the center foliation of f has codimension 2, or 2. the center leaves of f are simply connected leaves and the unstable foliation of f is one-dimensional.
Cite
@article{arxiv.1104.5464,
title = {Partially hyperbolic diffeomorphisms with compact center foliations},
author = {Andrey Gogolev},
journal= {arXiv preprint arXiv:1104.5464},
year = {2012}
}
Comments
22 pages, 1 figure. In the second version an error was corrected, the exposition was improved, new references added