On Algebraic Knots I : Computatability of Their Jones Polynomials(Knots and soft-matter physics: Topology of polymers and related topics in physics, mathematics and biology)

Abstract

We prove that the Jones polynomial of any Conway algebraic link diagram with n crossings can be computed in O(n^2) time. In particular, the Jones polynomial of any Montesinos link and two-bridge knot or link with minimum crossing number n can be computed in O(n^2) time.