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 …

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 …

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 …

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 …

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, …

The group scheme G_a here is the one-dimensional additive group.