The J(k, l) knots, often called the double twist knots, are a subclass of two-bridge knots which contains the twist knots. We show that the A-polynomial of these knots can be determined by an explicit resultant. We present this resultant in two different ways. We determine a recursive definition for the A-polynomials of the J(4, 2n) and J(5, 2n) knots, and for the canonical component of the A-polynomials of the J(2n, 2n) knots. Our work also recovers the A-polynomials of the J(1, 2n) knots, and the recursive formulas for the A-polynomials of the A(2, 2n) and A(3, 2n) knots as computed by Hoste and Shanahan.
|Original language||English (US)|
|Number of pages||35|
|Journal||New York Journal of Mathematics|
|State||Published - Sep 8 2015|
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- 2-bridge knot