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Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].

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Third de Rham cohomology group for the simply connected 4-manifolds

This is a question that has emerged from a discussion about some topological properties of spacetimes. Suppose that $M$ is a (Hausdorff, paracompact) smooth, orientable, connected, simply connected 4 …