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Results tagged with differential-topology
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user 123144
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
0
answers
248
views
Embeddings of exotic spheres
Let $\{S^n_u \mid u\in \text{some indexing set} \}$ be the set of all non-diffeomorphic $n$-spheres. Define $k_u$ to be the smallest number such that there exists a smooth embedding $S^n_u\hookrightar …
- 251
9
votes
1
answer
511
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Is the diffeomorphism group of the Euclidean space generated by two simpler subgroups?
Consider the group $\mathrm{Diff}(\mathbb R^n)$ of smooth diffeomorphisms. It has two interesting subgroups:
the orthogonal group $O(n)$,
the group of "diffeomorphisms applied along each axis" $\math …
- 251