On the AJ conjecture for cables of the figure eight knot

2014/05/16 by Anh T. Tran, Tran, Anh T. · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #Connective tissue disorders research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Primary 57N10 #Quantum Algebra (math.QA) #Secondary 57M25 #math.GT #math.QA #msc:57M25 #msc:57N10

paper · pdf · doi:10.48550/arxiv.1405.4055

New York Journal of Mathematics 20 (2014) 727-741

openalex publication_date 2014/05/16 · arxiv created 2014/09/02 · arxiv updated 2014/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ± 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| ≥ 9.

Citations

• Quantizations of Character Varieties and Quantum Knot Invariants
• On the AJ conjecture for knots
• Knot state asymptotics I, AJ Conjecture and abelian representations

Cited by

• On the AJ conjecture for cables of twist knots

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