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Results tagged with differential-topology
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user 3969
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”.
5
votes
Accepted
Question about exotic spheres
A exotic sphere is (by definition) a differentiable manifold. So if you want to consider the tetrahedron, you have to specify, what differentiability at one of the edges means. As soon as you specifie …
- 11.1k
3
votes
Artin groups whose graphs differ by one edge and coverings
Let $A_{\Gamma'}$ be the group asoociated to any graph $\Gamma'$.
Concerning your first question I can show that there is a short exact sequence
$$1\rightarrow F \rightarrow A_{\Gamma \setminus e}\r …
- 11.1k
7
votes
Accepted
Criteria for extending vector field on sphere to ball
View $B^{n}$ as $(S^{n-1}\times[0,1])/(S^{n-1}\times \{1\})$. This means that an extension of a map from $B^{n}$ to somewhere is just an extension to $S^{n-1}\times [0,1]$ which is constant on the oth …
- 11.1k
3
votes
Accepted
Topology of maps between fibers of vector bundles
If both bundles were trivial, say $X\times \mathbb{R}^n\rightarrow X$ and $Y\times \mathbb{R}^n\rightarrow Y$ one could just take $X\times Y\times M(m,n,\mathbb{R})$.
Different choices of trivializati …
- 11.1k