Uniqueness of the smooth structure on the four-sphere

Determine whether the four-sphere S^4 has a unique smooth structure up to diffeomorphism.

Background

The paper notes that the existence of complex structures on products involving S4 can depend on the underlying smooth structure. It therefore identifies the uniqueness, up to diffeomorphism, of the smooth structure on S4 as an unresolved foundational issue relevant to the broader context of Calabi-type complex-structure questions.

References

Whether S4 has a unique smooth structure up to diffeomorphism remains unknown .

— A Complex Structure on $T^2\times S^4$: The Genus-One Case of Calabi's Problem  (2610.06067 - Gao et al., 5 Oct 2026) in Section 1, Introduction