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

Author: Razvan Gelca
Journal: Proc. Amer. Math. Soc. 130 (2002), 1235-1241
MSC (1991): Primary 57M25, 58B30, 46L87
Published electronically: September 14, 2001
MathSciNet review: 1873802
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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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Additional Information

Razvan Gelca
Affiliation: Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409 – and – Institute of Mathematics of the Romanian Academy, Bucharest, Romania

Keywords: Kauffman bracket, Jones polynomial, A-polynomial, noncommutative geometry
Received by editor(s): May 9, 2000
Received by editor(s) in revised form: October 23, 2000
Published electronically: September 14, 2001
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2001 American Mathematical Society