Maximal Thurston–Bennequin number of two-bridge links

Abstract

We compute the maximal Thurston–Bennequin number for a Legendrian two-bridge knot or oriented two-bridge link in standard contact ${ℝ}^3$, by showing that the upper bound given by the Kauffman polynomial is sharp. As an application, we present a table of maximal Thurston–Bennequin numbers for prime knots with nine or fewer crossings.