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Results tagged with differential-topology
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user 89425
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
346
views
Open non-parallelizable 4-manifolds
Let $M$ be a connected orientable open 4-manifold (noncompact, without boundary).
Is it possible for $M$ to be non-parallelizable ?
If yes, what example of such $M$ is there ?
[EDIT : The answer …
- 361
6
votes
4
answers
1k
views
On a parallelizable manifold, is there always a frame satisfying $[X_i,X_j]=0$?
[This question was asked on MSE, but got no answers, I thought it could be more appropriate here]
Let $M$ be a parallelizable manifold.
Is there always a global frame $(X_i)$ such that $[X_i,X_j]=0 …
- 361
13
votes
2
answers
3k
views
Spin^c structures on manifolds with almost complex structure
Let $M$ be a smooth even-dimensional manifold.
Is it true that for each almost-complex structure $J$ on $M$ there exists a canonical spin$^c$ structure $S_J$ associated to $J$ ?
(I've read this som …
- 361