Heegaard Floer homologies and contact structures

Abstract

Given a contact structure on a closed, oriented three-manifold $Y$, we describe an invariant which takes values in the three-manifold's Floer homology $\HFa$. This invariant vanishes for overtwisted contact structures and is non-zero for Stein fillable ones. The construction uses of Giroux's interpretation of contact structures in terms of open book decompositions, and the knot Floer homologies introduced in math.GT/0209056.

22 pages, 3 figures

References in corpus (4)

• Heegaard Floer homology and alternating knots
• Holomorphic disks and three-manifold invariants: properties and applications
• Holomorphic triangles and invariants for smooth four-manifolds
• Holomorphic disks and knot invariants

Cited by in corpus (34)

• Heegaard Floer homology and alternating knots
• Knot Floer homology detects fibred knots
• Corrigendum to "Knot Floer homology detects fibred knots"
• Bounds for the Thurston-Bennequin number from Floer homology
• Ozsvath-Szabo invariants and tight contact three-manifolds, I
• Khovanov module and the detection of unlinks
• On the existence of tight contact structures on Seifert fibered 3-manifolds
• Longitude Floer homology and the Whitehead double
• Seifert fibered contact three-manifolds via surgery
• A contact invariant in sutured monopole homology
• Tight contact structures and genus one fibered knots
• Dehn surgery, rational open books and knot Floer homology
• A combinatorial description of the Heegaard Floer contact invariant
• Planar open books and Floer homology
• Dehn Twists in Heegaard Floer Homology
• Comultiplicativity of the Ozsvath-Szabo contact invariant
• Khovanov homology, open books, and tight contact structures
• On the equivalence of contact invariants in sutured Floer homology theories
• Holomorphic disks and knot invariants
• Capping off open books and the Ozsvath-Szabo contact invariant
• On Transverse Knots and Branched Covers
• Symplectic rational blow-down along Seifert fibered 3-manifolds
• Thurston norm, fibered manifolds and twisted Alexander polynomials
• Symmetries and adjunction inequalities for knot Floer homology
• Contact Ozsvath-Szabo Invariants and Giroux Torsion
• Khovanov homology and tight contact structures
• Transverse knots, branched double covers and Heegaard Floer contact invariants
• On contact surgery and knot Floer invariants
• On overtwisted, right-veering open books
• Notes on the contact Ozsvath--Szabo invariants
• Admissible transverse surgery does not preserve tightness
• Tight contact structures on some small Seifert fibered 3--manifolds
• On Legendrian surgeries between lens spaces
• Closed 3-braids are nearly fibred