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An evaluation of a link polynomial

Published online by Cambridge University Press:  24 October 2008

A. S. Lipson
A. S. Lipson
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge
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Extract

There exists for each oriented link L in the 3-sphere a unique 2-variable Laurent polynomial defined uniquely by the following:

(i) PU = 1 for the unknot U

(ii) ,

where L+, L− and L0 are identical outside a ball and inside are as shown in Figure 1. See [1] and [2].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 2 , September 1986 , pp. 361 - 364
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1] Freyd, P., Yetter, D., Hoste, J., Lickorish, W. B. R., Millet, K. and Ocneanu, A.. A new polynomial invariant of knots and links. Bull. A.M.S. 12 (1985), 239–246.CrossRefGoogle Scholar
[2] Lickorish, W. B. R. and Millett, K. C.. A polynomial invariant of oriented links. (To appear.)Google Scholar
[3] Lickorish, W. B. R. and Millett, K. C.. Some evaluations of link polynomials (To appear.)Google Scholar
[4] Rolfsen, D.. Knots and Links (Publish or Perish Inc., 1976).Google Scholar