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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Legendrian knots and polynomial invariants


Author: Emmanuel Ferrand
Journal: Proc. Amer. Math. Soc. 130 (2002), 1169-1176
MSC (1991): Primary 53C15, 57M25
Published electronically: September 14, 2001
MathSciNet review: 1873793
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Abstract: It is proved in this note that the analogues of the Bennequin inequality which provide an upper bound for the Bennequin invariant of a Legendrian knot in the standard contact three dimensional space in terms of the least degree in the framing variable of the HOMFLY and the Kauffman polynomials are not sharp. Furthermore, the relationships between these restrictions on the range of the Bennequin invariant are investigated, which leads to a new simple proof of the inequality involving the Kauffman polynomial.


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Additional Information

Emmanuel Ferrand
Affiliation: Institut Fourier, BP 74, 38402 St Martin d’Hères Cedex, France
Email: emmanuel.ferrand@ujf-grenoble.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06153-6
PII: S 0002-9939(01)06153-6
Keywords: Contact topology, polynomial invariants of knots
Received by editor(s): July 11, 2000
Received by editor(s) in revised form: October 24, 2000
Published electronically: September 14, 2001
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2001 American Mathematical Society