Splitting spheres for unlinked $S^2$'s in $S^4$

TL;DR

This paper proves the existence of infinitely many distinct splitting spheres for two unlinked, unknotted 2-spheres in 4-dimensional space, answering a previously open question.

Contribution

It establishes the existence of infinitely many non-isotopic splitting spheres for unlinked $S^2$'s in $S^4$, advancing understanding of 4-manifold topology.

Findings

Existence of infinitely many non-isotopic splitting spheres

Addresses a question by Hughes, Kim, and Miller

Contributes to the classification of embeddings in 4-manifolds

Abstract

We show that there exist infinitely many pairwise non-isotopic splitting spheres for two unlinked, unknotted $S^2$'s in $S^4$. This answers a question posed by Hughes, Kim, and Miller.