The coloured Jones function


Melvin, PM and Morton, HR ORCID: 0000-0002-8524-2695 (1995) The coloured Jones function Communications in Mathematical Physics, 169 (3). pp. 501-520. ISSN 0010-3616, 1432-0916

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Abstract

The invariants J<inf>K,k</inf> of a framed knot K coloured by the irreducible SU(2)<inf>q</inf>-module of dimension k are studied as a function of k by means of the universal R-matrix. It is shown that when J<inf>K,k</inf> is written as a power series in h with q=eh, the coefficient of hd is an odd polynomial in k of degree at most 2 d+1. This coefficient is a Vassiliev invariant of K. In the second part of the paper it is shown that as k varies, these invariants span a d-dimensional subspace of the space of all Vassiliev invariants of degree d for framed knots. The analogous questions for unframed knots are also studied. © 1995 Springer-Verlag.

Item Type: Article
Additional Information: ## TULIP Type: Articles/Papers (Journal) ## official_url: <Go to ISI>://A1995QY58100003
Uncontrolled Keywords: 4903 Numerical and Computational Mathematics, 4904 Pure Mathematics, 49 Mathematical Sciences
Depositing User: Symplectic Admin
Date Deposited: 23 Jan 2017 10:08
Last Modified: 28 Feb 2026 23:40
DOI: 10.1007/BF02099310
Related Websites:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3005309
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