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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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Are normal deformations of an embedding open in the $C^{\infty}$-space of embeddings of a co...

Not to leave this question open: The question as posed is wrong by the example I gave. However the example I gave is in some sense the maximum which can go wrong. More precisely small normal deformat …
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Are normal deformations of an embedding open in the $C^{\infty}$-space of embeddings of a co...

Let $M$ be a compact smooth manifold (closed, for simplicity), $n\in\mathbb{N}$ and equip the space of embeddings $Emb(M,\mathbb{R^n})$ wih the Whitney-$C^{\infty}$-topology. (The weak and the strong …
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