English

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.

Keywords

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