Brunnian links of 3-balls in the 4-sphere

TL;DR

This paper constructs infinitely many Brunnian links of 3-balls in the 4-sphere for any number of components, using splitting spheres and providing a new proof for a key existence result.

Contribution

It introduces a method to generate infinitely many Brunnian links of 3-balls in 4-spheres and offers a new proof for the existence of splitting spheres in this context.

Findings

Construction of infinitely many Brunnian links in S^4

New proof of splitting spheres for trivial 2-sphere links in S^4

Extension of Brunnian link theory to 4-dimensional topology

Abstract

For each integer $n\ge 2$, we construct infinitely many $n$-component Brunnian links of 3-balls in $S^4$. Our main tool is the third author's result on the existence of splitting spheres for the trivial two-component link of $2$-spheres in $S^{4}$; we also give a new proof of this.