Cobordism in dimension 4
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Theorem (Wall's Theorem on h-cobordism). If two smooth simply-connected 4-manifolds $M$ and $N$ have isotopic intersection forms, then they are h-cobordant.
Theorem (Freedman's 4-dimensional h-cobordism). Suppose two simply-connected 4-manifolds $M$ and $N$ are h-cobordant through a simply-connected 5-manifold $W$. Then $W$ is homeomorphic to $M\times[0,1]$. In particular, $M$ and $N$ are homeomorphic.
Corollary. If two smooth simply-connected 4-manifolds $M$ and $N$ have isomorphic intersection forms, then they are homeomorphic.
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