On the AJ conjecture for cables of the figure eight knot
نویسندگان
چکیده
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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تاریخ انتشار 2014