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Results tagged with principal-bundles
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user 16852
A principal $G$-bundle, where $G$ denotes any topological group, is a fiber bundle $\pi :P → X$ together with a continuous right action $P × G → P$ such that $G$ preserves the fibers of $P$ and acts freely and transitively on them.
1
vote
Spaces of symplectic embeddings: Bundle? Smoothness?
This is not an answer, but I hope it helps. Let $P = {\rm Emb}((M,\omega), (N,\sigma))$. The quotient $Q = P / {\rm Symp}(M,\omega)$ appears to be the set of symplectic submanifolds of $N$ which are …
- 614
0
votes
Lie algebra version of principal bundle?
Building upon Peter's answer, An Atiyah algebroid, or transitive Lie algebroid is one answer to your question.
- 614
1
vote
Why does the group act on the right on the principal bundle?
As David Roberts said (and you seem to already know), left vs right is just convention.
In the same way that Riemannian geometry literature was influenced by the role it played in general relativity …
- 614
9
votes
A geometric interpretation of the Levi-Civita connection?
This avoids use of Christoffel symbols and index argument by re-characterizing the torsion free property. The following is one definition for a torsion-free connection. Let $\tau:TM \to M$ be the ta …
- 614