The coloured Jones function and Alexander polynomial for torus knots
- 1 January 1995
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 117 (1), 129-135
- https://doi.org/10.1017/s0305004100072959
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.Keywords
This publication has 3 references indexed in Scilit:
- ON THE INVARIANTS OF TORUS KNOTS DERIVED FROM QUANTUM GROUPSJournal of Knot Theory and Its Ramifications, 1993
- Invariants of Links and 3-Manifolds From Skein Theory and From Quantum GroupsPublished by Springer Science and Business Media LLC ,1993
- Ribbon graphs and their invaraints derived from quantum groupsCommunications in Mathematical Physics, 1990