Communications in Mathematical Physics

, Volume 169, Issue 3, pp 501–520 | Cite as

The coloured Jones function

  • P. M. Melvin
  • H. R. Morton


The invariantsJ K,k of a framed knotK coloured by the irreducibleSU(2) q -module of dimensionk are studied as a function ofk by means of the universalR-matrix. It is shown that whenJ K,k is written as a power series inh withq=e h , the coefficient ofh d is an odd polynomial ink of degree at most 2d+1. This coefficient is a Vassiliev invariant ofK. In the second part of the paper it is shown that ask varies, these invariants span ad-dimensional subspace of the space of all Vassiliev invariants of degreed for framed knots. The analogous questions for unframed knots are also studied.


Colour Neural Network Statistical Physic Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • P. M. Melvin
    • 1
  • H. R. Morton
    • 2
  1. 1.Department of MathematicsBryn Mawr CollegeBryn MawrUSA
  2. 2.Department of Pure MathematicsUniversity of LiverpoolLiverpoolUK

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