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Results tagged with differential-topology
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user 14037
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
Accepted
Smooth submanifold of a complex manifold with invariant tangent space under multiplication b...
Let $f : N \to M$ denote the immersion.
Since $f_*TN$ is invariant under $I$ where $I$ is the underlying almost complex structure of $M$, it induces an almost complex structure $I'$ on $N$.
Applying N …
- 1,829
5
votes
Accepted
Curvature of principal bundle
I'll use $\Omega \in \Omega^2(P,\mathfrak{g})$ to denote the curvature tensor of $\omega$.
One way of identifying these two expressions is through Cartan's structure equation
$$\Omega = d\omega + \fra …
- 1,829