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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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Is transverse intersection continuous?

Let $S_0$ be a smooth compact $k$-dimensional manifold with boundary and $\mathcal{E}_{\rm p}(S_0, \mathbb{D}^n)$ be the space of smooth proper embeddings into the unit disk in $\mathbb{R}^n$ with the …
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