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Seifert circles and knot polynomials

Published online by Cambridge University Press:  24 October 2008

H. R. Morton
H. R. Morton
Affiliation:
Department of Pure Mathematics, University of Liverpool
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 1 , January 1986 , pp. 107 - 109
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Bennequin, D.. Entrelacements et équations de Pfaff. Astérisque 107–8 (1983), 87–161.Google Scholar
[2]Franks, J. and Williams, R. F.. Braids and the Jones polynomial. (Preprint 1985).Google Scholar
[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), 239–246.CrossRefGoogle Scholar
[4]Lickorish, W. B. R. and Millett, K. C.. A polynomial invariant of oriented links. (Preprint 1985.)Google Scholar
[5]Morton, H. R.. Closed braid representatives for a link, and its 2-variable polynomial. (Preprint, Liverpool 1985.)Google Scholar