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Results tagged with smooth-manifolds
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user 4362
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].
19
votes
Accepted
Fundamental group of a compact manifold
Every compact manifold has the homotopy type of a finite CW-complex, and a finite CW-complex has finitely presented fundamental group by van Kampen's theorem.
- 29.2k
10
votes
Topological Classification of Four-Manifolds
Suppose you can classify all open 4-manifolds. In particular you can classify all manifolds of the form $M^4 - pt$ where $M^4$ is a closed 4-manifold, and consequently you can classify all closed 4-m …
- 29.2k
8
votes
What should be taught in a 1st course on smooth manifolds?
I think there are two ways to approach a first course on manifolds: one can focus on either their geometry or their topology.
If you want to focus on geometry, then I think Anton Petrunin's suggestio …