A property of the skein polynomial with an application to contact geometry

Details A property of the skein polynomial with an application to contact geometry A property of the skein polynomial with an application to contact geometry

2000-08-16

arxiv.org/abs/math/0008126v2

J. Differential Geom. 77(3) (2007), 555--566.

Mathematics

Geometric Topology

7 pages

Scientific paper

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.

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