Brunnian links of 3-balls in the 4-sphere
Seungwon Kim, Gheehyun Nahm, Alison Tatsuoka

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 , we construct infinitely many -component Brunnian links of 3-balls in . Our main tool is the third author's result on the existence of splitting spheres for the trivial two-component link of -spheres in ; we also give a new proof of this.
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Taxonomy
TopicsGeometric and Algebraic Topology · Geometric Analysis and Curvature Flows · Point processes and geometric inequalities
