The Dold-Whitney theorem and the Sato-Levine invariant

TL;DR

This paper links the Dold-Whitney theorem to the Sato-Levine invariant, providing a mod 4 obstruction to certain 2-component links being slice, thus connecting bundle classification with link concordance.

Contribution

It establishes a novel connection between the Dold-Whitney theorem and the Sato-Levine invariant, revealing a new obstruction in link theory.

Findings

Identifies a mod 4 obstruction to sliceness of 2-component links with trivial linking number.

Shows this obstruction coincides with the reduction of the Sato-Levine invariant.

Provides a new perspective on link concordance using bundle classification.

Abstract

We use the Dold-Whitney theorem classifying $SO(3)$-bundles over a 4-complex to give a mod 4 obstruction to a 2-component link of trivial linking number being slice. It turns out that this coincides with the reduction of the Sato-Levine invariant.