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Results tagged with principal-bundles
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user 1708
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.
4
votes
Accepted
Is there an easy example of group action where the slice theorem produces a non-trivial prin...
Consider the usual $G = S^1$ action on $S^2$ given by rotations. This action respects the antipodal map, so descends to a $G$ action on $M = \mathbb{R}P^2$. Let $p\in M$ be any point on the "equator …
- 6,546
9
votes
A nontrivial principal bundle which satisfies Leray-Hirsch theorem
Suppose $M = S^n$ is a sphere with $n$ odd and at least $5$. Pick your favorite Lie group $G$ for which $\pi_{n-1}(G)$ is non-trivial. (Many examples may be found here. For example, for any $n > 3$ …
- 6,546
4
votes
Accepted
Principal bundles from a fibration of homogeneous spaces
I call such bundles "homogeneous bundles", but it's not a totally standard terminology.
It is true that the map $G/H\rightarrow G/H'$ is a fiber bundle map with fiber $H/H'$. One way to see this is t …
- 6,546