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The Colored Jones Polynomial and the A-Polynomial of Knots

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Preprint
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arXiv ID: math/0407521
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arXiv
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Abstract

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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