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


Anh T. Tran

On the AJ conjecture for cables of the figure eight knot

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Published: August 12, 2014
Keywords: Colored Jones polynomial, A-polynomial, AJ conjecture, figure eight knot
Subject: Primary 57N10. Secondary 57M25

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 (r,2)-cable of the figure eight knot satisfies the AJ conjecture if r is an odd integer satisfying |r| ≧ 9.

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Department of Mathematical Sciences, The University of Texas at Dallas, 800 W Campbell Rd, FO 35, Richardson TX 75080