The maximal Thurston--Bennequin number of a doubled knot

Abstract

We show that an upper bound for the maximal Thurston--Bennequin number of any double of a knot $K$ given by the Kauffman polynomial is sharp if the bound is sharp for $K$. In particular, we give formulas for the maximal Thurston--Bennequin numbers of positive doubles of torus knots and two-bridge knots.