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Dec 31, 2023 at 22:48 comment added mme Maybe you'll like the explanation I gave here.
Dec 31, 2023 at 18:59 history edited YCor
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Dec 31, 2023 at 18:58 comment added Danny Ruberman I don't really get the question. As you've described it, M is the projectivization of the complex line bundle of Chern class 1 over $S^2$, and hence is exactly the non-trivial $S^2$ bundle over $S^2$. Are you asking why that's a connected sum of $\pm \mathbb{C}P^2$?
S Dec 31, 2023 at 13:18 history suggested Zerox CC BY-SA 4.0
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Dec 31, 2023 at 12:04 review Suggested edits
S Dec 31, 2023 at 13:18
Dec 31, 2023 at 11:43 comment added Mikhail Katz Cross-posted at math.stackexchange.com/questions/4834301/… (question closed).
Dec 31, 2023 at 9:51 history edited Dimpi Paul CC BY-SA 4.0
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S Dec 31, 2023 at 9:46 review First questions
Dec 31, 2023 at 10:50
S Dec 31, 2023 at 9:46 history asked Dimpi Paul CC BY-SA 4.0