Self-duality and differentiable structures on the connected sum of complex projective planes

Pedersen, Henrik; Poon, Yat Sun

doi:10.1090/S0002-9939-1994-1195729-1

Self-duality and differentiable structures on the connected sum of complex projective planes
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by Henrik Pedersen and Yat Sun Poon PDF

Proc. Amer. Math. Soc. 121 (1994), 859-864 Request permission

Abstract:

It is proved that if the twistor space of a self-dual four-manifold of positive scalar curvature contains a real effective divisor of degree two, then the four-manifold is diffeomorphic to the connected sum $n\mathbb {C}{P^2}$ of n complex projective planes for some n. It follows that if the four-manifold is known to be homeomorphic to $4\mathbb {C}{P^2}$, then it is also diffeomorphic to $4\mathbb {C}{P^2}$.

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