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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
Posted:
September 14, 2001
MathSciNet review:
1873802
Full-text PDF Free Access
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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
Email:
rgelca@math.ttu.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-01-06157-3
PII:
S 0002-9939(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
Posted:
September 14, 2001
Communicated by:
Ronald A. Fintushel
Article copyright:
© Copyright 2001 American Mathematical Society
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