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

A. Stoimenow Kyoto University

Differential Geometry mathscidoc:1609.10045

Journal of Differential Geometry, 77, (3), 523-534, 2007
We prove a finiteness property of the values of the skein polynomial of homogeneous knots that allows us 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). We also give a short proof that there are only finitely many such knots that have given genus and given braid index.
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@inproceedings{a.2007a,
  title={A PROPERTY OF THE SKEIN POLYNOMIAL WITH AN APPLICATION TO CONTACT GEOMETRY},
  author={A. Stoimenow},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909102702668463702},
  booktitle={Journal of Differential Geometry},
  volume={77},
  number={3},
  pages={523-534},
  year={2007},
}
A. Stoimenow. A PROPERTY OF THE SKEIN POLYNOMIAL WITH AN APPLICATION TO CONTACT GEOMETRY. 2007. Vol. 77. In Journal of Differential Geometry. pp.523-534. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909102702668463702.
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