TY - JOUR

T1 - On the relation between the A-polynomial and the Jones polynomial

AU - Gelca, Rǎzvan

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

KW - A-polynomial

KW - Jones polynomial

KW - Kauffman bracket

KW - Noncommutative geometry

UR - http://www.scopus.com/inward/record.url?scp=0035994158&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-01-06157-3

DO - 10.1090/S0002-9939-01-06157-3

M3 - Article

AN - SCOPUS:0035994158

SN - 0002-9939

VL - 130

SP - 1235

EP - 1241

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

ER -