The AJ-conjecture and cabled knots over the figure eight knot

Abstract

We show that most cabled knots over the figure eight knot in $S^3$ satisfy the AJ-conjecture, in particular, any $(r,s)$-cabled knot over the figure eight knot satisfies the $AJ$-conjecture if $r$ is not a number between $-4s$ and $4s$.

24 pages

References in corpus (5)

• On the characteristic and deformation varieties of a knot
• Difference equation of the colored Jones polynomial for torus knot
• A cabling formula for the colored Jones polynomial
• The colored Jones polynomial and the A-polynomial for twist knots
• The AJ-conjecture and cabled knots over torus knots

Cited by in corpus (5)

• A Cable Knot and BPS-Series
• The AJ-Conjecture for Cables of Two Bridge Knots
• A Cable Knot and BPS-Series II
• On the AJ conjecture for cables of the figure eight knot
• The strong AJ conjecture for the figure eight knot