A New Algorithm for Numerical Calculation of Link Invariants

TL;DR

This paper introduces a novel numerical algorithm for calculating link polynomials, specifically the Jones polynomial, efficiently aiding in the topological analysis of knots in three dimensions using computational methods.

Contribution

The paper presents a new algorithm that computes derivatives of the Jones polynomial with computational complexity proportional to N^α, improving numerical knot analysis.

Findings

Efficient computation of Jones polynomial derivatives.

Computational complexity scales as N^α.

Provides a new tool for topological knot analysis.

Abstract

We propose a new method for numerical calculation of link plynomials for knots given in 3 dimensions. We calculate derivatives of the Jones polynomial in a computational time proportional to $N^{\alpha}$ with respect to the system size $N$ . This method gives a new tool for determining topology of knotted closed loops in three dimensions using computers.