Heegaard Floer invariants of Legendrian knots in contact   three--manifolds
  We define invariants of null--homologous Legendrian and transverse knots in contact 3--manifolds. 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. 
Paolo Lisca, Peter Ozsv\'ath, Andr\'as I. Stipsicz and Zolt\'an   Szab\'o