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

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

2000-04-25

arxiv.org/abs/math/0004158v1

Mathematics

Quantum Algebra

LATEX, 6 pages

Scientific paper

In previous joint work with Frohman and Lofaro a noncommutative generalization of the A-polynomial of a knot was introduced, consisting of a finitely generated ideal of polynomials (the noncommutative A-ideal) in the quantum plane. The present paper shows that the noncommutative A-ideal of a knot, together with finitely many of its colored Jones polynomials determines all other colored Jones polynomials. Also, for particular knots, such as the unknot and the trefoil, the noncommutative A-ideal completely determines all colored Jones polynomials.

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