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 -