 

Kathleen L. Petersen
Apolynomials of a family of twobridge knots view print


Published: 
September 8, 2015 
Keywords: 
Apolynomial, 2bridge knot 
Subject: 
57M25, 57M27 


Abstract
The J(k,l) knots, often called the double twist knots, are a subclass of twobridge knots which contains the twist knots.
We show that the Apolynomial 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 Apolynomials of the J(4,2n) and J(5,2n) knots, and for the canonical component of the Apolynomials of the J(2n,2n) knots. Our work also recovers the Apolynomials of the J(1,2n) knots, and the recursive formulas for the Apolynomials of the A(2,2n) and A(3,2n) knots as computed by Hoste and Shanahan.


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


Author information
Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA
petersen@math.fsu.edu

