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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”.

2 votes
1 answer
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Extending diffeomorphisms of some faces of the standard $n$- simplex to a diffeomorphism of ...

I would be grateful if you could help me with the following question: Let $n\in \mathbb{N}$ and $k\in \{1, \ldots, n+1\}$. For every $i=1, ..., k$ let $f_i : \partial_i \Delta^n \rightarrow \partial_ …
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1 vote

A relative version of Ehresmann's theorem

I think that one can prove the relative version of Ehresmann's lemma (and also versions for manifolds with corners, which is my interest) without any technology as follows: Let us first recall the fo …
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