Computing A-polynomials using Puiseux expansions
by
David Boyd
University of British Columbia

The A-polynomial of a knot complement is a two variable polynomial A(x,y) with integer coefficients that is notoriously difficult to compute in general. The computation requires the elimination of variables in a large set of polynomial equations. We present a method of computing this polynomial using Puiseux expansions about certain geometrically meaningful solutions of the equations and then using linear algebra. We give some examples of A-polynomials that were previously inaccessible by earlier methods.

Date received: April 28, 2004