On the Conway potential function introduced by Kauffman

TL;DR

This paper proves that Kauffman's Conway potential function is a valid link invariant and is equivalent to Hartley's potential function, using Murakami's axioms for the multivariable Alexander polynomial.

Contribution

It establishes the invariance of Kauffman's potential function and its equivalence to Hartley's, clarifying their relationship in knot theory.

Findings

Kauffman's potential function is a link invariant.

Kauffman's potential function equals Hartley's potential function.

Proof uses Murakami's axioms for the multivariable Alexander polynomial.

Abstract

We show two results about the Conway potential function which is known as the normalized multivariable Alexander polynomial. We first show that the Conway potential function introduced by Kauffman in "Formal Knot Theory" is indeed a link invariant. Next we show that Kauffman's potential function equals Hartley's potential function. We will prove it by using Murakami's axioms for the multivariable Alexander polynomial.