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ISSN 1088-6826(e) ISSN 0002-9939(p)

Maximal Bennequin numbers and Kauffman polynomials of positive links

Author(s): Toshifumi Tanaka
Journal: Proc. Amer. Math. Soc. 127 (1999), 3427-3432.
MSC (1991): Primary 57M50, 57M25
Posted: May 6, 1999
MathSciNet review: 1616601
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Abstract: By using results of Yamada and of Yokota, concerning link diagrams and link polynomials, we give some relationships between maximal Bennequin numbers and Kauffman polynomials of positive links.

References:

1.: D. Rolfsen, Knots and links, Publish or Perish, Inc. (1976). MR 58:24236
2.: L. H. Kauffman, On knots, Ann. of Math. Studies 115. Princeton Univ. Press (1987). MR 89c:57005
3.: S. Yamada, The minimal number of Seifert circles equals to the braid index of a link, Invent. Math., Vol. 89, (1987). MR 88f:57015
4.: J. Swiatkowski, On the isotopy of Legendrian knots, Ann. Glob. Anal. Geom. Vol. 10, pp. 195-207 (1992). MR 93m:57010
5.: Y. Yokota, Polynomial invariants of positive links, Topology, Vol. 31, No. 4, pp. 805-811 (1992). MR 93k:57028
6.: L. Rudolph, An obstruction to sliceness via contact geometry and ``classical" gauge theory, Invent. Math, Vol. 199, pp. 155-163 (1995). MR 95k:57013
7.: D. Fuchs, S. Tabachnikov, Invariants of Legendrian and transverse knots in the standard contact space, Topology, Vol. 36, No. 5, pp. 1025-1053 (1997). CMP 97:11
8.: S. Tabachnikov, Estimates for the Bennequin number of Legendrian links from state models for knot polynomials, Math. Res. Let. Vol. 4, pp. 143-156 (1997). CMP 97:08

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Additional Information:

Toshifumi Tanaka
Affiliation: Graduate School of Mathematics, Kyushu University, Hakozaki 6-10-1, Higashiku, Fukuoka, 812-8581 Japan
Email: ttanaka@math.kyushu-u.ac.jp

DOI: 10.1090/S0002-9939-99-04983-7
PII: S 0002-9939(99)04983-7
Keywords: Positive links, Bennequin number, Kauffman polynomial
Received by editor(s): September 27, 1997
Received by editor(s) in revised form: February 6, 1998
Posted: May 6, 1999
Communicated by: Ronald A. Fintushel
Copyright of article: Copyright 1999, American Mathematical Society

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