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I posted this question: http://mathoverflow.net/questions/119751/lie-groups-bundle/119794#119794 However I don't understand how he builds the isomorfism and the induced fiber bundle...

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Are you asking how to construct the associated bundle in general or only in this specific answer? Maybe it would be a good idea to elaborate this post into an actual question, in particular a reasonably self-contained one. – Martin Jan 25 at 14:30

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