Planar open books and Floer homology

Abstract

Giroux has described a correspondence between open book decompositions on a 3--manifold and contact structures. In this paper we use Heegaard Floer homology to give restrictions on contact structures which correspond to open book decompositions with planar pages, generalizing a recent result of Etnyre.

17 pages, 4 figures

References in corpus (4)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• Heegaard Floer homologies and contact structures
• Holomorphic triangles and invariants for smooth four-manifolds
• The Weinstein Conjecture for Planar Contact Structures in Dimension Three

Cited by in corpus (10)

• Ozsvath-Szabo invariants and tight contact three-manifolds, I
• Planar open books, monodromy factorizations, and symplectic fillings
• A Hierarchy of Local Symplectic Filling Obstructions for Contact 3-Manifolds
• Tight contact structures and genus one fibered knots
• Mapping class group relations, Stein fillings, and planar open book decompositions
• Planar open books with four binding components
• Contact surgery and supporting open books
• Contact Structures on Plumbed 3-Manifolds
• Stein fillings of homology $3$-spheres and mapping class groups
• Hypersurface singularities and virtually overtwisted contact structures