Singular link concordance implies link homotopy in codimension $\ge 3$

TL;DR

This paper proves that in codimension at least 3, singular link concordance implies link homotopy, extending classical results and providing new analogues for link maps.

Contribution

It establishes a singular analogue of the Concordance Implies Isotopy theorem for link maps in high codimension, enhancing understanding of link homotopy.

Findings

Singular link concordance implies link homotopy in codimension ≥ 3

Extension of classical concordance-isotopy results to singular link maps

Independent proof for spherical link maps by P. Teichner

Abstract

We prove the analogue of the Concordance Implies Isotopy in Codimension $\ge 3$ Theorem for link maps, together with some other its singular analogues. In the case of spherical link maps, a stronger result was independently obtained by P. Teichner (by different methods).