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Results tagged with fibre-bundles
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user 147463
for questions about fiber bundles, including structure groups, principal bundles, and spaces of sections.
2
votes
1
answer
735
views
Principal G-bundles over the circle
To edify my understanding of fiber bundles with structure groups, I was currently trying to reconcile two classifications (in a particular case). For simplicity, I'm taking the base to be $S^1$ and th …
- 1,225
3
votes
Accepted
Principal G-bundles over the circle
Okay, I figured out my mistake! I was trying to use left-actions everywhere, but we need some left and some right. This comes up when constructed associated bundles: if you have a left $G$-space $F$, …
- 1,225
3
votes
1
answer
155
views
When is compactness of fiber components an open condition?
Consider a smooth map $f:M\rightarrow N$ between smooth manifolds.
Ehresmann's theorem states that if $f$ is a proper submersion, then it is locally trivializable; in particular, this implies that nea …
- 1,225