Maximal Thurston–Bennequin numbers of alternating links

We show that the upper bound of the maximal Thurston–Bennequin number for an oriented alternating link given by the Kauffman polynomial is sharp. As an application, we confirm a question of Ferrand. We also give a formula of the maximal Thurston–Bennequin number for all two-bridge links. Finally, we introduce knot concordance invariants derived from the Thurston–Bennequin number and the Maslov number of a Legendrian knot.