THE COLORED JONES FUNCTION AND ALEXANDER POLYNOMIAL FOR TORUS KNOTS

MORTON, HR ORCID: 0000-0002-8524-2695 (1995) THE COLORED JONES FUNCTION AND ALEXANDER POLYNOMIAL FOR TORUS KNOTS MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 117 (1). pp. 129-135. ISSN 0305-0041, 1469-8064

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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 J<inf>K, k</inf>(h)= Σ^∞<inf>d=0</inf>α<inf>d</inf>(k) h^d, where J<inf>K, k</inf>(h) is the SU(2)<inf>g</inf>quantum invariant of K when coloured by the irreducible module of dimension k, and q = e^his the quantum group parameter. In this paper I show that the explicit formula does give the Alexander polynomial when K is any torus knot. © 1995, Cambridge Philosophical Society. All rights reserved.

Item Type:	Article
Uncontrolled Keywords:	4902 Mathematical Physics, 4903 Numerical and Computational Mathematics, 4904 Pure Mathematics, 49 Mathematical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	23 Jan 2017 10:09
Last Modified:	22 May 2026 18:55
DOI:	10.1017/S0305004100072959
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3005308
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