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Results tagged with smooth-manifolds
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user 12482
Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].
8
votes
When (why) did we allow manifolds to be non-Hausdorff and/or non-second countable?
Non-Hausdorffness shows up in several contexts when dealing with Lie groupoids: the integration (Lie's 3rd Theorem) for Lie algebroids to Lie groupoids will typically produce a non-Hausdorff one, if i …
- 8,098
9
votes
1
answer
2k
views
Automorphism group of a fiber bundle surjects onto diffeomorphism group?
This should surely be well-known by I have not been able to find a good reference to the following question: Given a smooth fiber bundle $\pi\colon P \longrightarrow M$ over a smooth manifold $M$ with …
- 8,098
10
votes
How special are homogeneous spaces?
I suppose you want the action to be transitive as your title suggests. In this case, a classical theorem of Mostow (in 1950 for surfaces, in 2005 in general) says that for a compact homogeneous space …
- 8,098