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Results tagged with differential-topology
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user 4362
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”.
74
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3
answers
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Can analysis detect torsion in cohomology?
Take, for example, the Klein bottle K. Its de Rham cohomology with coefficients in $\mathbb{R}$ is $\mathbb{R}$ in dimension 1, while its singular cohomology with coefficients in $\mathbb{Z}$ is $\ma …
- 29.2k
38
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Smooth homotopy theory
Let us define the nth smooth homotopy group of a smooth manifold $M$ to be the group $\pi_n^\infty(S^k)$ of smooth maps $S^n \to S^k$ modulo smooth homotopy. Of course, some care must be taken to def …
- 29.2k