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Results tagged with principal-bundles
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user 4790
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.
7
votes
What is "Data" involved in a mathematical construction?
"Data" is the plural form of the Latin word "datum", which means, among other things, "thing that is given". Viewed this way, it makes perfect sense, doesn't it?
- 27k
5
votes
Accepted
Principal bundles in the etale and Zariski topology and extensions of the structure group
The answer is more or less as Jason says, but the proof is very easy, and does not require any cohomological machinery. If $P \to X$ is a $G$-torsor, then $P/G' \to X$ is a $G''$-torsor, hence it is Z …
- 27k
8
votes
Accepted
pullback diagram of principal bundles
In the stated generality, it is false; for example, suppose that $G_1$ and $G_2$ are trivial groups, $P = B \times G$ (here $B$ is the base), and the maps $P_1 \to P$ and $P_2 \to P$ are given by two …
- 27k
5
votes
Representations of \pi_1, G-bundles, Classifying Spaces
Atiyah's statement makes sense only if one gives $U(1)$ the discrete topology, otherwise it is just plain false (continuous $U(1)$-bundles are classified topologically by their first Chern class, whic …
- 27k