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$CP^2$ and $\bar{CP^2}$ are not diffeomorphic since they have non-isomorphic intersection forms. so why do we call the latter $CP^2$ with reverse orientation? it seems like we are not just reversing a given orentation on $CP^2$ to get $\bar {CP^2}$.

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    Maybe im misunderstanding your question but the two spaces are certainly diffeomorphic (its the same manifold!). The point is that there is no orientation preserving diffeomorphism from $CP^2$ to $\bar{CP}^2$. In other words there is no orientation reversing automorphism of $CP^2$. – Tim kinsella Nov 10 '13 at 02:41

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