On the contact class in heegaard floer homology

Abstract

We present an alternate description of the Ozsváth-Szabó 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. © 2009 J. differential geometry.