The Colored Jones Polynomial and the A-Polynomial of Knots

Details The Colored Jones Polynomial and the A-Polynomial of Knots The Colored Jones Polynomial and the A-Polynomial of Knots

2004-07-30

arxiv.org/abs/math/0407521v4

Mathematics

Geometric Topology

Typos and minor mistakes corrected. To appear in Advances in Mathematics

Scientific paper

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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