On the AJ conjecture for cables of the figure eight knot
arXiv:1405.4055
Abstract
The AJ conjecture relates the A-polynomial and the colored Jones polynomial of a knot in the 3-sphere. It has been verified for some classes of knots, including all torus knots, most double twist knots, (-2,3,6n \pm 1)-pretzel knots, and most cabled knots over torus knots. In this paper we study the AJ conjecture for (r,2)-cables of a knot, where r is an odd integer. In particular, we show that the AJ conjecture holds true for (r,2)-cables of the figure eight knot, where r is an odd integer satisfying |r| \ge 9.
New York Journal of Mathematics 20 (2014) 727-741
References in corpus (5)
- On the characteristic and deformation varieties of a knot
- The AJ-conjecture and cabled knots over the figure eight knot
- Quantizations of Character Varieties and Quantum Knot Invariants
- The AJ-conjecture and cabled knots over torus knots
- Knot state asymptotics I, AJ Conjecture and abelian representations