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Results tagged with differential-topology
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user 1227
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”.
1
vote
Accepted
Poincaré–Bendixson Theorem on a compact, connected, orientable, two-dimensional manifold
To address your two questions:
Why is $q \in N$?
If I understand correctly, they could have (and should have) just started with $q \in \Sigma$, since for any $q \in \Sigma$ the orbit $\phi_t(x)$ app …
- 6,581
5
votes
Accepted
Can orientation preserving diffeomorphism in $\mathbb{R}^d$ be presented by flowmap of dynam...
No, this is usually not possible. There's a previous MO question discussing this, but to add to the material there:
A time-one map $\phi_1$ commutes with the 1-parameter family of diffeomorphisms $\p …
- 6,581
8
votes
Accepted
Fibers of generic smooth maps between manifolds of equal dimension
Yes, the claim is true, and here's a reference. For $M$ compact, your condition is satisfied by a "finite mapping." Such finite mappings form a residual set when $\dim M \leq \dim N$. See pp. 167-169 …
- 6,581