Hostname: page-component-7c8c6479df-ws8qp Total loading time: 0 Render date: 2024-03-28T11:29:42.442Z Has data issue: false hasContentIssue false

Jones polynomials and classical conjectures in knot theory. II

Published online by Cambridge University Press:  24 October 2008

Kunio Murasugi
Affiliation:
University of Toronto, Canada

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
Copyright
Copyright © Cambridge Philosophical Society 1987

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]Gordon, C. McA. and Litherland, R. A.. On the signature of a link. Invent. Math. 47 (1978), 5369.CrossRefGoogle Scholar
[2]Jones, V. F. R.. A polynomial invariant for knots via von Neumann algebras. Bull. Amer. Math. Soc. 89 (1985), 103111.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), 277303.Google Scholar
[5]Murasugi, K.. On a certain numerical invariant of link types. Trans. Amer. Math. Soc. 117 (1965), 387422.Google Scholar
[6]Murasugi, K.. Jones polynomials of alternating links. Trans. Amer. Math. Soc. 295 (1986), 147174.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