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Let $(M,g)$ be an irreducible compact and simply connected Ricci-flat Riemannian four-manifold. My first questions are as follows: A) Is there a classification of the possible homeomorphism types of ...

Edit: One can also assume $M,N$ compact in the following, and that $M$ is equipped with a Riemannian metric as well. Incorporated Mike's suggestion. Sard's theorem says that for every smooth map $f: ...