Polyak-Viro formulas for coefficients of the Conway polynomial

TL;DR

The paper presents Polyak-Viro arrow diagram formulas for calculating Conway polynomial coefficients, simplifying the process by expressing it as a state sum over knot diagram crossings, related to Jaeger's HOMFLY polynomial model.

Contribution

It introduces a new arrow diagram formula for Conway polynomial coefficients, connecting it to state sum models and simplifying previous computational methods.

Findings

Provides explicit Polyak-Viro formulas for Conway polynomial coefficients.

Expresses the Conway polynomial as a simplified state sum over knot crossings.

Links the Conway polynomial computation to Jaeger's state model for the HOMFLY polynomial.

Abstract

We describe the Polyak-Viro arrow diagram formulas for the coefficients of the Conway polynomial. As a consequence, we obtain the Conway polynomial as a state sum over some subsets of the crossings of the knot diagram. It turns out to be a simplification of a special case of Jaeger's state model for the HOMFLY polynomial.