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 $4s$.

arXiv comment24 pages

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Cited by in corpus (6)

• A Cable Knot and BPS-Series
• Knot Cabling and the Degree of the Colored Jones Polynomial
• 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