Planar open book decompositions and contact structures
Symplectic Geometry
2007-05-23 v3 Geometric Topology
Abstract
In this note we observe that while all overtwisted contact structures on compact 3--manifolds are supported by planar open book decompositions, not all contact structures are. This has relevance to invariants of contact structures and also to the Weinstein conjecture via work of Abbas Cieliebak and Hofer.
Cite
@article{arxiv.math/0404267,
title = {Planar open book decompositions and contact structures},
author = {John B. Etnyre},
journal= {arXiv preprint arXiv:math/0404267},
year = {2007}
}
Comments
10 pages, 3 figures. Proof that overtwisted contact structures are supported by open books is corrected. Various improvements in the exposition