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