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Sep 27, 2017 at 15:58 comment added Michael Albanese The blowup of $\mathbb{CP}^n$ at a point is diffeomorphic to $\mathbb{CP}^n\#\overline{\mathbb{CP}^n}$, not $\mathbb{CP}^n\#\mathbb{CP}^n$. For $n$ even, the two spaces are not even homotopy equivalent.
Sep 27, 2017 at 11:43 history edited Michael Albanese CC BY-SA 3.0
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Sep 27, 2017 at 8:09 comment added Faith @Dima I just have searched this book and find the proof. Thank you for your comment
Sep 27, 2017 at 6:57 history asked Faith CC BY-SA 3.0