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Results tagged with smooth-manifolds
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user 126667
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].
20
votes
Least number of charts to describe a given manifold
To answer your last question, the least number of charts needed to cover any orientable 2-manifold is 2. Consider the usual embedding of an orientable surface Σ in R3 which is symmetric across the pl …
- 25.2k
43
votes
Are there two non-homotopy equivalent spaces with equal homotopy groups?
All of these examples involve a bit of cleverness, so I thought I'd point out a more straightforward way to construct counterexamples. If $X$ is any space, we can build a space $X' = K(\pi_0 X, 0) \t …
- 25.2k