Spanning 3-discs in the 4-sphere pushed into the 5-disc

TL;DR

This paper proves that any two smooth collections of spanning 3-discs for the trivial 2-link in the 4-sphere become smoothly isotopic rel. boundary after being pushed into the 5-disc, advancing understanding of high-dimensional link isotopies.

Contribution

It establishes a new isotopy result for spanning 3-discs in the 4-sphere when embedded into the 5-disc, extending previous high-dimensional link theory.

Findings

Any two smooth collections of spanning 3-discs are isotopic rel. boundary in D^5.

The result applies specifically to the trivial 2-link in S^4.

The proof involves pushing the discs into a higher-dimensional disk to achieve isotopy.

Abstract

I prove that any two smooth collections of spanning 3-discs for the trivial 2-link in $S^4$ become smoothly isotopic rel. boundary after pushing them into $D^5$.