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

Clayton McDonald

geometric topology

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

arXiv:2607.27619

summary

The paper provides the first examples of homology 3‑spheres that can be smoothly embedded in the product manifold S²×S² but cannot be embedded in the 4‑sphere S⁴, answering K3 problem 4.28b.

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 $S^{4}$ .

1 page

Topics & keywords

#smooth embeddings #homology 3-spheres #4-manifolds #embedding problems #k3 problemS^2×S^2smooth embeddinghomology 3-sphereK3 problem 4.28b

An S2×S2 embedding

Abstract

Topics & keywords

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