On invariants of link maps in dimension four

TL;DR

This paper confirms the well-definedness of a proposed link homotopy invariant in four dimensions and shows its equivalence to another invariant when adapted, advancing understanding of link map invariants.

Contribution

It establishes the well-definedness of Li's invariant and demonstrates its equivalence to Schneiderman-Teichner's invariant when adapted, clarifying their relationship.

Findings

Li's invariant $oldsymbol{ extomega}$ is well-defined.

The invariant $oldsymbol{ au}$ of Schneiderman-Teichner coincides with $oldsymbol{ extomega}$ when adapted.

Provides a better understanding of link homotopy invariants in four dimensions.

Abstract

We affirmatively address the question of whether the proposed link homotopy invariant $\omega$ of Li is well-defined. It is also shown that if one wishes to adapt the homotopy invariant $\tau$ of Schneiderman-Teichner to a link homotopy invariant of link maps, the result coincides with $\omega$.