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Local Trivialality Triviality of an Associated Bundle |
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Local Trivialality of an Associated BundleI 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 the total space $P \times_{\rho} \mathbb{C}^n$ is locally trivial.
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