A property of the skein polynomial with an application to contact geometry
Abstract
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 R3), and a give a short proof that there are only finitely many among these knots that have given genus and given braid index.
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