Universal weight systems and the Melvin-Morton expansion of the colored Jones knot invariant

1996/05/02 by Arkady Vaintrob, Vaintrob, Arkady
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Quantum Algebra (math.QA) #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9605003

20 pages, LaTeX with bezier.sty

arxiv created 1996/05/02 · openalex publication_date 1996/05/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic expansion of the colored Jones polynomial (the Melvin-Morton expansion) using a recursion formula for the deframed universal weight system for the sl(2) Lie algebra. Combined with the formula for the universal weight system for the Lie superalgebra gl(1|1) (which corresponds to the Alexander-Conway knot polynomial) this formula gives a very short proof of the Melvin-Morton conjecture relating the colored Jones invariant and the Alexander-Conway polynomial of knots.

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