On the AJ conjecture for knots

Abstract

We confirm the AJ conjecture [Ga04] that relates the A-polynomial and the colored Jones polynomial for those hyperbolic knots satisfying certain conditions. In particular, we show that the conjecture holds true for some classes of two-bridge knots and pretzel knots. This extends the result of the first author in [Le06] where he established the AJ conjecture for a large class of two-bridge knots, including all twist knots. Along the way, we explicitly calculate the universal character ring of the knot group of the (-2,3,2n+1)-pretzel knot and show that it is reduced for all integers n.

References in corpus (1)

• On the characteristic and deformation varieties of a knot

Cited by in corpus (11)

• Twisted Alexander polynomials of 2-bridge knots for parabolic representations
• The AJ-conjecture and cabled knots over the figure eight knot
• Knot contact homology and representations of knot groups
• Quantum Knot Invariants
• The universal character ring of some families of one-relator groups
• The AJ-conjecture and cabled knots over torus knots
• The SL(2,C) Casson invariant for knots and the $\hat{A}$-polynomial
• The AJ-Conjecture for Cables of Two Bridge Knots
• Affine cubic surfaces and character varieties of knots
• Shadows and quantum invariants
• On the AJ conjecture for cables of the figure eight knot