The Colored Jones Polynomial and the A-Polynomial of Knots

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.

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

References in corpus (1)

• On the characteristic and deformation varieties of a knot

Cited by in corpus (1)

• On the Head and the Tail of the Colored Jones Polynomial