2013/10/26 by Garoufalidis, Stavros, Vuong, Thao · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1310.7143
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 \citeGL2. We illustrate our results with sample computations.