4
votes
3answers
208 views
What is a good way to think about a fundamental field on a principal G-bundle?
Let $\pi:P \rightarrow M$ be a principal $G$-bundle, and let $A \in \mathfrak{g}$, where the Lie algebra of $G$ is indicated. The fundamental field $A$# used to define connections …
3
votes
1answer
152 views
Principal bundles and associated vector bundles, the case of the complex projective space (1,0)-forms
As can be guessed from some of my previous questions, I'm trying to understand, at the moment, the relationship between principal and their associated vector bundles. To this end I …
1
vote
4answers
153 views
Local Triviality of an Associated Bundle
I was reading this question link text
and can't seem to see why, if $\pi: P \to B$ is a principle $G$-bundle and $$\rho:G \to GL_n(\mathbb{C})$$ is a representation of $G$, then th …
2
votes
1answer
92 views
Transition Functions of the Principal Bundle $SU(2) \to \mathbb{CP}^1$
I've been trying to understand principal bundles, and to that end have been looking at the bundle
$$
\pi: SU(2) \to \mathbb{CP}^1,~~~ (a_{ij}) \mapsto [a_{11},a_{21}],
$$
with fib …
12
votes
3answers
373 views
Sheaf Description of G-Bundles
Now, among algebraic geometers, at least, it is well known that there is an equivalence between locally free O_X-modules of rank n and vector bundles of rank n. So, equivalently, …
3
votes
1answer
109 views
Over which schemes can there exist non-trivial G_a bundles?
The group scheme G_a here is the one-dimensional additive group.
