Bounds for the Thurston–Bennequin number from Floer homology

Abstract

Using a knot concordance invariant from the Heegaard Floer theory of Ozsváth and Szabó, we obtain new bounds for the Thurston–Bennequin and rotation numbers of Legendrian knots in $S^3$. We also apply these bounds to calculate the knot concordance invariant for certain knots.