Skip to main content
    • Aa
    • Aa

The coloured Jones function and Alexander polynomial for torus knots

  • H. R. Morton (a1)

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.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[4] M. Rosso and V. F. R. Jones . On the invariants of torus knots derived from quantum groups, Journal of Knot Theory and its Ramifications 2 (1993), 97112.

[5] N. Y. Reshetikhin and V. G. Turaev . Ribbon graphs and their invariants derived from quantum groups. Comm. Math. Phys. 127 (1990), 126.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 20 *
Loading metrics...

Abstract views

Total abstract views: 45 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 25th September 2017. This data will be updated every 24 hours.