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I'm studying Donaldson Invariants from chapter 9 of The wild world of 4-manifolds by Scorpan, and I'm looking for an example where they're used to distinguish two 4-manifolds which are homeomorphic but not diffeomorphic.

I know that these invariants are quite hard to compute, and honestly I don't even know where to start in order to find such manifolds; are there any "famous examples" well-known in the literature?

Thank you.

Andrews
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Bargabbiati
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  • 'are there any "famous examples" well-known in the literature?' - examples of 4-manifold pairs that are homeomorphic but not diffeomorphic? If the answer is yes, you can cook up very easy examples. I think what you're interested in are 4-manifold pairs that are both smooth but have different smooth structure. Please correct me if I'm mistaken. – J. Moeller Mar 30 '19 at 21:36
  • Yes, I'm interested in smooth 4-manifolds that do not admit smooth structures such that they are diffeomorphic, but that are homeomorphic; in the question when I write manifold I always mean "smooth" manifold. – Bargabbiati Mar 30 '19 at 21:53
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    See https://arxiv.org/pdf/0812.1883.pdf – Nick L Apr 04 '19 at 12:24

1 Answers1

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Within the first three pages of this [1] you can find many examples from algebraic geometry that are homeomorphic but not diffeomorphic.

[1] 4-manifolds Which are Homeomorphic but not Diffeomorphic by David Gay

Student
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