An $S^2 \times S^2$ embedding

Clayton McDonald

An $S^2 \times S^2$ embedding

Geometric Topology 2026-07-30 v1

Authors: Clayton McDonald

Abstract

In this note, we give a positive answer to K3 problem 4.28b, giving the first examples of homology 3-spheres that embed smoothly in $S^2 \times S^2$ but not $S^4$ .

Cite

@article{arxiv.2607.27619,
  title  = {An $S^2 \times S^2$ embedding},
  author = {Clayton McDonald},
  journal= {arXiv preprint arXiv:2607.27619},
  year   = {2026}
}

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