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Results tagged with smooth-manifolds
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user 1708
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].
8
votes
When does a submersion have connected fibers?
If $M$ and $N$ are both compact, then the submersion $F$ can be thought of as a fiber bundle map with fiber $F^{-1}(p)$ for any $p\in N$. Then one can apply the long exact sequence of homotopy groups …
- 6,546
24
votes
1
answer
3k
views
Characteristic classes of sphere bundles over spheres in terms of clutching functions
I'm trying to understand Milnor's proof of the existence of exotic 7-spheres.
Milnor finds his examples among $S^{3}$ bundles over $S^{4}$ (with structure group $SO(4)$ ). Such a bundle can be descr …
- 5,530
10
votes
Classification problem for non-compact manifolds
I just wanted to mention that the fact that the word problem is "hard" for groups doesn't mean that there can be no classification for manifolds of dimension $\geq$ 4.
The problem is that the word "h …
- 6,546