Generalized Alexander Polynomial Invariants

TL;DR

This paper introduces an algorithm to derive generalized Alexander polynomial invariants of knots and links using q,p-numbers from two-parameter quantum algebra, unifying several classical invariants through parametrization.

Contribution

The paper presents a novel algorithm that derives various polynomial invariants of knots and links from a unified algebraic framework involving q,p-numbers.

Findings

The algorithm can produce generalized Alexander polynomials.

It recovers HOMFLY polynomials through specific parametrization.

Jones polynomials are also obtainable via the same algorithm.

Abstract

We propose an algorithm which allows to derive the generalized Alexander polynomial invariants of knots and links with the help of the q,p-numbers, appearing in bosonic two-parameter quantum algebra. These polynomials turn into HOMFLY ones by applying special parametrization. The Jones polynomials can be also obtained by using this algorithm.