Signature Jumps and Alexander Polynomials for Links

TL;DR

This paper establishes a relationship between the signature function jumps of a link and the roots of its first nonzero higher Alexander polynomial, providing new insights into link invariants.

Contribution

It introduces a novel connection between signature jumps and Alexander polynomial roots, advancing the understanding of link invariants.

Findings

Signature jumps correspond to roots of the Alexander polynomial.

Provides a new method to analyze link signatures.

Enhances the theoretical framework of link invariants.

Abstract

We relate the jumps of the signature function of a link to the roots of its first nonzero higher Alexander polynomial.