New York Journal of Mathematics
Volume 21 (2015) 847-881


Kathleen L. Petersen

A-polynomials of a family of two-bridge knots

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Published: September 8, 2015
Keywords: A-polynomial, 2-bridge knot
Subject: 57M25, 57M27

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.


This work was partially supported by Simons Foundation grant #209226.

Author information

Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA