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Results tagged with differential-topology
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user 391
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”.
9
votes
Are the associative grassmannian and the quaternionic projective plane diffeomorphic?
To expand on Oscar's answer: the principal $SO(4)$ bundle over
$G_2/SO(4)$ gives us
$$ \qquad \qquad \qquad \ldots \to \pi_2(G_2) \to \pi_2(G_2/SO(4)) $$
$$ \to \pi_1(SO(4)) \to \pi_1(G_2) \to \pi_1(G …
- 27.9k
6
votes
Is it true that all sphere bundles are some double of disk bundle?
The connected double cover of $S^1$ (boundary of the Möbius strip) is an $S^0$ bundle that is not the double of the unique $0$-disc bundle over $S^1$.
- 27.9k
5
votes
On the generalized Gauss-Bonnet theorem
Mathai and Quillen have a theorem that computes the Euler characteristic as an integral of a form defined using a section of and a connection on the tangent bundle. If one scales the section by a fact …
- 27.9k