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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Henrik Pedersen and Yat Sun Poon
Journal: Proc. Amer. Math. Soc. 121 (1994), 859-864
MSC: Primary 32L25; Secondary 32J17, 53C56, 57R55
MathSciNet review: 1195729
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1195729-1
PII: S 0002-9939(1994)1195729-1
Article copyright: © Copyright 1994 American Mathematical Society