Milnor invariants via unipotent Magnus embeddings

TL;DR

This paper introduces a new approach to computing Milnor invariants of links using unipotent Magnus embeddings, providing a diagrammatic method and refining higher-degree invariants.

Contribution

It redefines Milnor invariants through central group extensions and unipotent Magnus embeddings, offering new computational techniques and refinements for higher degrees.

Findings

Developed a diagrammatic computation method for Milnor invariants.

Computed the first non-vanishing invariants of the Milnor link.

Refined the original Milnor invariants for higher degrees.

Abstract

We reconfigure the Milnor invariant of links in terms of central group extensions and unipotent Magnus embeddings. We also develop a diagrammatic computation of the invariant and compute the first non-vanishing invariants of the Milnor link and of several other links. Moreover, we refine the original Milnor invariants of higher degree.