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Jones polynomials and classical conjectures in knot theory. II

Published online by Cambridge University Press:  24 October 2008

Kunio Murasugi
Kunio Murasugi
Affiliation:
University of Toronto, Canada
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Extract

Let L be an alternating link and be its reduced (or proper) alternating diagram. Let w() denote the writhe of [3], i.e. the number of positive crossings minus the number of negative crossings. Let VL(t) be the Jones polynomial of L [2]. Let dmaxVL(t) and dminVL(t) denote the maximal and minimal degrees of VL(t), respectively. Furthermore, let σ(L) be the signature of L [5].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 102 , Issue 2 , September 1987 , pp. 317 - 318
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

REFERENCES

[1]Gordon, C. McA. and Litherland, R. A.. On the signature of a link. Invent. Math. 47 (1978), 53–69.CrossRefGoogle Scholar
[2]Jones, V. F. R.. A polynomial invariant for knots via von Neumann algebras. Bull. Amer. Math. Soc. 89 (1985), 103–111.CrossRefGoogle Scholar
[3]Kauffman, L.. State models for knot polynomials. (To appear.)Google Scholar
[4]Murasugi, K.. On alternating knots. Osaka Math. J. 12 (1960), 277–303.Google Scholar
[5]Murasugi, K.. On a certain numerical invariant of link types. Trans. Amer. Math. Soc. 117 (1965), 387–422.Google Scholar
[6]Murasugi, K.. Jones polynomials of alternating links. Trans. Amer. Math. Soc. 295 (1986), 147–174.Google Scholar
[7]Murasugi, K.. Jones polynomials and classical conjectures in knot theory. Topology (in the Press).Google Scholar
[8]Thistlethwaite, M. B.. Kauffman's polynomial and alternating links. Preprint.Google Scholar