Kirby Problem 4.128

TheoremDB P10904 · topology

Source catalogue assessmentAs of 2026-09-08Source & evidence ↓

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Problem statement

What is the structure of 4-manifolds that admit a Riemannian metric of positive scalar curvature? There are variations of this problem for different classes of manifolds.

(a) Is every closed simply connected PSC 4-manifold diffeomorphic to a connected sum of copies of $\mathbb{CP}^{2}, \mathbb{CP}^{2}$ , and $S^{2} \times S^{2}$ ?

(b) What is the structure of non-simply connected closed PSC 4-manifolds?

(d) Which non-compact 4-manifolds have a complete PSC metric with uniformly positive scalar curvature?

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Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.

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References

[1]TheoremDB P10904 link

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