The strong AJ conjecture for the figure eight knot

Abstract

Motivated by the theory of quantum A-ideals of Frohman-Gelca-LoFaro, the theory of q-holonomicity of quantum invariants of Garoufalidis-Le and the AJ conjecture of Garoufalidis, Sikora formulated the strong AJ conjecture which relates the A-ideal and recurrence ideal of a knot in the 3-sphere. This conjecture has been verified for all torus knots and most of their cables. In this paper, we verify the strong AJ conjecture for the figure eight knot.

arXiv comment11 pages

References in corpus (3)

• 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