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Results tagged with lie-groups
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user 4362
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
34
votes
Example of a manifold which is not a homogeneous space of any Lie group
Atiyah and Hirzebruch gave a rather dramatic answer to your question in their paper "Spin Manifolds and Group Actions": if $M$ is a compact smooth spin manifold of dimension $4k$ whose $\hat{A}$-genus …
- 29.2k
6
votes
Is the Lie algebra-valued curvature two-form on a principal bundle P the curvature of a vect...
To the extent that I can keep all this stuff straight, I find it helpful to inform my intuition with the "path lifting" point of view for connections.
Let $\pi: F \to M$ be any smooth fiber bundle. …
- 29.2k