Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-19T14:48:53.323Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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