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G acts freely on P,
π(p 1) = π(p 2) if and only if there exists g ∈ G such that p 1 g = p 2,
P is locally trivial over M, i.e., for every m ∈ M there exists a neighborhood U of m and a map F u : π-1(U) → G such that F u (pg) = (F u (p))g and such that the map Ψ : π-1(U) → U × G taking p to (π(p), F u (p)) is a diffeomorphism.
KeywordsShort Exact Sequence Principal Bundle Connection Form Horizontal Lift Bundle Isomorphism
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