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Results tagged with principal-bundles
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user 47391
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.
3
votes
1
answer
730
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Is a closed basic 2-form on a principal $S^1$ bundle the curvature of a connection?
Suppose one has an $S^1$ principal bundle $p: P\rightarrow M$, and a closed 2-form $F$ on $M$. Then the pullback form $p^*F$ is closed, vanishes on vertical vectors, and is invariant under the action …
- 787
4
votes
1
answer
376
views
Parallel Transport on Hypersurface Spinor Bundle
So this has been driving me up a wall. I'm trying to digest parts of the Parker & Taubes paper, "On Witten's Proof of the Positive Energy Theorem." Here's a link:
https://projecteuclid.org/download/p …
- 787
1
vote
Parallel Transport on Hypersurface Spinor Bundle
I now believe that the statement in question (from the paper), "... the Riemannian connection $\bar\nabla$ of $M$... is compatible with $<\,,\,>$ but not with $(\,,\,)$" is false. It seems that both p …
- 787