A stability conjecture for the colored Jones polynomial

Stavros Garoufalidis; Thao Vuong

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arXiv · 1310.7143

A stability conjecture for the colored Jones polynomial

Stavros Garoufalidis·Thao Vuong

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Abstract

We formulate a stability conjecture for the coefficients of the colored Jones polynomial of a knot, colored by irreducible representations in a fixed ray of a simple Lie algebra, and verify it for all torus knots and all simple Lie algebras of rank $2$. Our conjecture is motivated by a structure theorem for the degree and the coefficients of a $q$-holonomic sequence of polynomials given in [Ga2] and by a stability theorem of the colored Jones polynomial of an alternating knot given in \cite{GL2}. We illustrate our results with sample computations.

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Stavros Garoufalidis, Thao Vuong. 2013-10-26. A stability conjecture for the colored Jones polynomial. https://arxiv.org/abs/1310.7143

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