  We prove a finiteness property of the values of the skein polynomial of
homogeneous knots which allows to establish large classes of such knots to have
arbitrarily unsharp Bennequin inequality (for the Thurston-Bennequin invariant
of any of their Legendrian embeddings in the standard contact structure of
R^3), and a give a short proof that there are only finitely many among these
knots that have given genus and given braid index.
