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

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

Published electronically:
September 14, 2001

MathSciNet review:
1873802

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Abstract | References | Similar Articles | Additional Information

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

Email:
rgelca@math.ttu.edu

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

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