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Results tagged with differential-topology
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user 59235
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”.
6
votes
1
answer
136
views
Existence of isotopy preserving the action
Let $\gamma_1$ and $\gamma_2$ be simple closed curves in $R^4.$ Let $\lambda= x_1 dy_1+ x_2dy_2.$ Suppose that $\int_{\gamma_1} \lambda= \int_{\gamma_2} \lambda.$
I am looking for a reference for …
- 937
5
votes
1
answer
682
views
Topology of surfaces and mean curvature
The Gauss-Bonnet theorem characterizes the topology of surfaces by means of their Gaussian curvature.
Do there exist results characterizing the topology of surfaces embedded in $\mathbf{R}^3$ via th …
- 937
12
votes
1
answer
2k
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Morse theory in infinite dimensions
It seems that people often talk of "doing Morse theory" on loop spaces in two quite different contexts.
Case 1: When one does Morse theory on a loop space $\Omega(M; p,q)$ using the energy functiona …
- 937
8
votes
0
answers
173
views
Topological restrictions from mean curvature bounds
Alexandrov's Theorem says that a compact constant mean curvature hypersurface embedded in $\mathbb{R}^{n+1}$ must be a round sphere.
What happens when the mean curvature is small, or bounded? (For in …
- 937