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Here the notions of the differentiable (smooth) manifold, differentiate (smooth) map, direct product of differentiable manifolds, tangent space and the differential of a map (the tangent map) are assumed to be known. Several other notions and theorems on differentiable manifolds will be recalled in the sequel.
KeywordsSemidirect Product Trivial Bundle Differentiable Manifold Differentiable Structure Tangent Algebra
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