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The coloured Jones function and Alexander polynomial for torus knots

Published online by Cambridge University Press:  24 October 2008

H. R. Morton
H. R. Morton
Affiliation:
Department of Pure Mathematics, University of Liverpool, PO Box 147, Liverpool, L69 3BX, U.K.
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Abstract

In [2] it was conjectured that the coloured Jones function of a framed knot K, or equivalently the Jones polynomials of all parallels of K, is sufficient to determine the Alexander polynomial of K. An explicit formula was proposed in terms of the power series expansion , where JK, k(h) is the SU(2)q quantum invariant of K when coloured by the irreducible module of dimension k, and q = eh is the quantum group parameter.

In this paper I show that the explicit formula does give the Alexander polynomial when K is any torus knot.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 117 , Issue 1 , January 1995 , pp. 129 - 135
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

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