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Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].

10 votes
Accepted

Reference Request: Compact manifolds with boundary have the homotopy type of a CW-complex

I have no idea at the moment where to find a reference for the specific result you seek. However, it can be deduced from the following fact: topological manifolds (paracompact and Hausdorff) are absol …
Ricardo Andrade's user avatar
6 votes

Is the space of diffeomorphisms homotopy equivalent to a CW-complex?

[Edit: Allen Hatcher posted an answer while I was writing this one. Both answers seem to use similar ideas. I will leave my answer here anyway.] $\newcommand{\Diff}{\operatorname{Diff}}$$\newcommand{ …
Ricardo Andrade's user avatar
30 votes
4 answers
3k views

Is the space of diffeomorphisms homotopy equivalent to a CW-complex?

Clarification: My question concerns the homotopy type of the space of $C^k$ diffeomorphisms with the compact-open $C^k$ topology, where $0< k \leq\infty$. I have stated my question below with $k=1$ fo …
Ricardo Andrade's user avatar
34 votes
1 answer
4k views

Strong Whitney embedding theorem for non-compact manifolds

$\newcommand{\RR}{\mathbb{R}}$The present question arises from some confusion on my part regarding the precise statement of the strong Whitney embedding theorem for non-compact manifolds. The strong …
Ricardo Andrade's user avatar