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The study of differentiable manifolds and differentiable maps. One fundamental problem is that of classifying manifolds up to diffeomorphism. Differential topology is what Poincaré understood as topology or “analysis situs”.

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Injectivity of homomorphism between homology groups of manifold and its boundary

I asked similar question before, after some modification, I have a new question. Suppose $M^{n\geq 4}$ is a connected compact smooth manifold with connected nonempty boundary. Suppose $i_*: H_1(\parti …
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