Communications in Mathematical Physics

, Volume 183, Issue 2, pp 291–306 | Cite as

Higher order terms in the Melvin-Morton expansion of the colored Jones polynomial

  • L. Rozansky


We formulate a conjecture about the structure of “upper lines” in the expansion of the colored Jones polynomial of a knot in powers of (q−1). The Melvin-Morton conjecture states that the bottom line in this expansion is equal to the inverse Alexander polynomial of the knot. We conjecture that the upper lines are rational functions whose denominators are powers of the Alexander polynomial. We prove this conjecture for torus knots and give experimental evidence that it is also true for other types of knots.


High Order Term Jones Polynomial Alexander Polynomial Rational Homology Sphere Skein Relation 
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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • L. Rozansky
    • 1
  1. 1.School of MathematicsInstitute for Advanced StudyPrincetonU.S.A.

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