On the relation between the A-polynomial and the Jones polynomial

Gelca, Răzvan

doi:10.1090/S0002-9939-01-06157-3

On the relation between the A-polynomial and the Jones polynomial
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by Răzvan Gelca

Proc. Amer. Math. Soc. 130 (2002), 1235-1241

DOI: https://doi.org/10.1090/S0002-9939-01-06157-3

Published electronically: September 14, 2001

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Abstract:

This paper shows that the noncommutative generalization of the A-polynomial of a knot, defined using Kauffman bracket skein modules, together with finitely many colored Jones polynomials, determines the remaining colored Jones polynomials of the knot. It also shows that under certain conditions, satisfied for example by the unknot and the trefoil knot, the noncommutative generalization of the A-polynomial determines all colored Jones polynomials of the knot.

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