# Change of trivialization

by Wideep   Last Updated April 15, 2019 10:20 AM

Let $$\pi:P\to M$$ a smooth $$G$$-principal bundle with action $$\beta:G\times P\to P$$, $$G$$ a Lie group and $$M$$ a diff. manifold. Let also $$T^*P$$ be its cotangent bundle and $$\sigma$$ be a section of this latter. I was wondering if a change of trivialization of the cotangent bundle may be seen as induced by a change of trivialization of $$P$$ and thus as given by the action of $$\beta_g$$ with $$g\in G$$, namely as the action over $$P$$ and the pull-back of the covector, like: $$(p,\sigma_p)\to(\beta_g(p),\beta^*_g\sigma_p).$$

Does it make sense?

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