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Results tagged with differential-topology
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user 5484
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”.
4
votes
Accepted
Smooth mapping from $\mathrm{RP}^2$ to $\mathbb{R}^3$ with nonsingular derivative
This is a famous problem that was solved by a doctoral student of David Hilbert named Werner Boy in 1901. The kind of mapping you are looking for is called an "immersion" (of its domain — the real pro …
- 2,858
5
votes
3
answers
343
views
Classification of surface bundles over surfaces
Can anyone recommend one place or a few places that describe what is known about the classification of (real) surface bundles over (real) surfaces?
Now, if the fibre F and the base B are both Hausdor …
- 2,858
1
vote
Theorems similar to Tischler fibering theorem
If a smooth compact oriented n-manifold M has a closed k-form that is not a coboundary, it then defines a non-trivial k-dimensional cohomology class, which is a kind of k-dimensional hole in M.
This i …
- 2,858
10
votes
What is a foliation and why should I care?
Here's why I care about foliations. It is always interesting when a structure can be expressed in terms of simpler structures. For instance a torus is the union of circles making it into a cartesian p …
- 2,858