We deﬁne invariants of null-homologous Legendrian and transverse knots in contact 3manifolds. The invariants are determined by elements of the knot Floer homology of the underlying smooth knot. We compute these invariants, and show that they do not vanish for certain non-loose knots in overtwisted 3-spheres. Moreover, we apply the invariants to ﬁnd transversely non-simple knot types in many overtwisted contact 3-manifolds.
Cite this article
Peter S. Ozsváth, Zoltán Szabó, Paolo Lisca, András I. Stipsicz, Heegard Floer invariants of Legendrian knots in contact three-manifolds. J. Eur. Math. Soc. 11 (2009), no. 6, pp. 1307–1363DOI 10.4171/JEMS/183