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.
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