Brunnian spanning 3-disks for the 2-unlink in the 4-sphere

TL;DR

This paper demonstrates that in the 4-sphere, the 2-component unlink can be spanned by infinitely many Brunnian 3-disks, revealing complex topological structures.

Contribution

It introduces the existence of infinitely many Brunnian spanning 3-disks for the 2-unlink in the 4-sphere, a novel topological construction.

Findings

Existence of infinitely many isotopy classes of Brunnian 3-disks

Brunnian property in higher-dimensional disk spans

Topological complexity of the 2-unlink in S^4

Abstract

We show that the $2$-component unlink in $S^4$ admits infinitely many isotopy classes of spanning $3$-disks that are Brunnian.