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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”.

5 votes
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3-sphere bundles over 4-sphere bound smooth disc bundles

I saw in the answer of this post: Is it true that all sphere bundles are boundaries of disk bundles? that a $S^3$-bundle over $S^4$ bounds a disc bundle over $S^4$ iff $O(4)\rightarrow Diff(S^3)$ is …
Renato Moreira's user avatar