On the existence of supporting broken book decompositions for contact forms in dimension 3
Dynamical Systems
2022-03-10 v4 Geometric Topology
Symplectic Geometry
Abstract
We prove that in dimension 3 every nondegenerate contact form is carried by a broken book decomposition. As an application we get that if M is a closed irreducible oriented 3-manifold that is not a graph manifold, for example a hyperbolic manifold, then every nondegenerate Reeb vector field on M has positive topological entropy. Moreover, we obtain that on a closed 3-manifold, every nondegenerate Reeb vector field has either two or infinitely many periodic orbits, and two periodic orbits are possible only on the sphere or on a lens space.
Keywords
Cite
@article{arxiv.2001.01448,
title = {On the existence of supporting broken book decompositions for contact forms in dimension 3},
author = {Vincent Colin and Pierre Dehornoy and Ana Rechtman},
journal= {arXiv preprint arXiv:2001.01448},
year = {2022}
}