On right-veering diffeomorphisms and contact class in Heegaard Floer homology

Abstract: We present an alternate deion of the Ozsv'ath-Szab'o
contact class in Heegaard Floer homology. Using our deion of the
contact class, we prove that if a contact structure $(M,\xi)$ 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.