On the contact class in Heegaard Floer homology

Abstract

We present an alternate description of the Ozsvath-Szabo contact class in Heegaard Floer homology. Using our contact class, we prove that if a contact structure (M,ξ) has an adapted open book decomposition whose page S is a once-punctured torus, then the monodromy is right-veering if and only if the contact structure is tight.

17 pages, figures are in color. Lemma added

References in corpus (1)

• Floer homology and knot complements

Cited by in corpus (6)

• Heegaard Floer invariants of Legendrian knots in contact three--manifolds
• Comultiplicativity of the Ozsvath-Szabo contact invariant
• Khovanov homology, open books, and tight contact structures
• Khovanov homology and tight contact structures
• Torsion and Open Book Decompositions
• Combinatorial proofs for basic properties of Ozsvath-Szabo invariant