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Post Closed as "off topic" by Ryan Budney, Agol, Dan Petersen, Andrew Stacey, S. Carnahan♦
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added open problem tag, removed a few less informative tags
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Is there a smooth $4$-manifold homeomorphic but not diffemorphic to $CP^2$?Is there a smooth $4$-manifold homeomorphic but not diffemorphic to $CP^2$? Are there known non-smooth examples homeomorphic $CP^2$?
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