Finite type invariants of knots via their Seifert matrices

TL;DR

This paper introduces a new filtration on Seifert matrices of knots, linking finite type invariants to the Alexander polynomial, thereby providing a novel algebraic approach to knot invariants.

Contribution

It defines a filtration on Seifert matrices related to Vassiliev invariants and expresses these invariants through Alexander polynomial coefficients.

Findings

Invariants from the filtration can be expressed by Alexander polynomial coefficients.

A new algebraic framework connects Seifert matrices to finite type invariants.

The filtration provides a structured way to study knot invariants.

Abstract

We define a filtration on the vector space spanned by Seifert matrices of knots related to Vassiliev's filtration on the space of knots. Further we show that the invariants of knots derived from the filtration can be expressed by coefficients of the Alexander polynomial.