On Conway's potential function for colored links

Abstract

The Conway potential function (CPF) for colored links is a convenient version of the multi-variable Alexander-Conway polynomial. We give a skein characterization of CPF, much simpler than the one by Murakami. In particular, Conway's `smoothing of crossings' is not in the axioms. The proof uses a reduction scheme in a twisted group-algebra ${\mathbb{P}}_n{B}_n$, where $B_n$ is a braid group and ${\mathbb{P}}_n$ is a domain of multi-variable rational fractions. The proof does not use computer algebra tools. An interesting by-product is a characterization of the Alexander-Conway polynomial of knots.

Cited by in corpus (5)

• On a Heegaard Floer theory for tangles
• Kauffman states and Heegaard diagrams for tangles
• A Non-Abelian Generalization of the Alexander Polynomial from Quantum ${\mathfrak{sl}}_3$
• Seifert-Torres Type Formulas for the Alexander Polynomial from Quantum ${\mathfrak{sl}}_2$
• On the skein polynomial for links