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The Colored Jones Polynomial and the A-Polynomial of Knots
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The Colored Jones Polynomial and the A-Polynomial of Knots
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We study relationships between the colored Jones polynomial and the A-polynomial of a knot. We establish for a large class of 2-bridge knots the AJ conjecture (of Garoufalidis) that relates the colored Jones polynomial and the A-polynomial. Along the way we also calculate the Kauffman bracket skein module of all 2-bridge knots. Some properties of the colored Jones polynomial of alternating knots are established.
Forward citations
Cited by 2 Pith papers
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Kauffman bracket skein module of the connected sum of two solid tori
The Kauffman bracket skein module of the connected sum of two genus-one handlebodies is determined over Z[q^{±1}].
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Two roles of Alexander in two Kashaev phases
Alexander polynomials appear in two opposite roles in two Kashaev phases of Chern-Simons theory due to co-existing branches in the quasiclassical limit with non-trivial versus vanishing classical actions.
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