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The Colored Jones Polynomial and the A-Polynomial of Knots

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arxiv math/0407521 v4 pith:XDH6AXJD submitted 2004-07-30 math.GT math.QA

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keywords coloredjonesknotspolynomiala-polynomialbridgealongalternating
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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.

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  1. Two roles of Alexander in two Kashaev phases

    hep-th 2026-05 unverdicted novelty 5.0 of 10

    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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