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Seifert circles and knot polynomials

  • H. R. Morton (a1)
Abstract

In this paper I shall show how certain bounds on the possible diagrams presenting a given oriented knot or link K can be found from its two-variable polynomial PK defined in [3]. The inequalities regarding exponent sum and braid index of possible representations of K by a closed braid which are proved in [5] and [2] follow as a special case.

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[1]Bennequin D.. Entrelacements et équations de Pfaff. Astérisque 1078 (1983), 87161.
[2]Franks J. and Williams R. F.. Braids and the Jones polynomial. (Preprint 1985).
[3]Freyd P., Yetter D., Hoste J., Lickorish W. B. R., Millett K. C. and Ocneanu A.. A new polynomial invariant of knots and links. Bull. Amer. Math. Soc. (N.S.) 12 (1985), 239246.
[4]Lickorish W. B. R. and Millett K. C.. A polynomial invariant of oriented links. (Preprint 1985.)
[5]Morton H. R.. Closed braid representatives for a link, and its 2-variable polynomial. (Preprint, Liverpool 1985.)
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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