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arXiv:math/0407521 [math.GT]AbstractReferencesReviewsResources

The Colored Jones Polynomial and the A-Polynomial of Knots

Thang T. Q. Le

Published 2004-07-30, updated 2006-03-27Version 4

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.

Comments: Typos and minor mistakes corrected. To appear in Advances in Mathematics
Categories: math.GT, math.QA
Subjects: 57M25
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