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Let $M$ be a manifold and let $U_{\alpha}$ and $U_{\beta}$ be coordinate charts with coordinates $x^{\alpha}$ and $x^{\beta}$, respectively.

How to show that $f_{\alpha} : U_{\alpha}\times\mathbb{R}^n\to TM_{|U_{\alpha}}$, $(p,a^{\alpha})\to\sum_{i} a^\alpha_i\frac{\partial}{\partial x^\alpha_i}|_{p}$ is a bundle isomorphism?

  • 0
    What is your question?2012-10-22
  • 0
    What is the relation of $U_\beta$? With what are you having trouble?2012-10-23

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