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Results tagged with differential-topology
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user 4008
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”.
3
votes
I was wondering if the set of singular loops is a (somewhere) submanifold of loop space?
The following argument I think should work to prove that the answer is no (though I haven't checked whether it really fits in with the proper definition): Consider a loop where three points of $S^1$ m …
- 22.6k
22
votes
"Largest" finite-dimensional Lie subgroups of Diff(S^n), are they known?
For 2) I think the following is an answer: Suppose $K$ is a compact Lie subgroup
of $\mathrm{Diff}(S^n)$ of dimension $\geq{n+1\choose 2}$. Being compact it is
the group of isometries of some Riemanni …
- 22.6k