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12
votes
Are submersions of differentiable manifolds flat morphisms?
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I suppose the next question is: does proving the special case above of a single g and h reduce the proof of flatness to algebraic manipulation? …
12
votes
Are submersions of differentiable manifolds flat morphisms?
Slightly reorganizing your definition of flatness, let n be a positive integer. … If the flatness property is true then it says that $g_y$ is contained in a finitely generated submodule of V, generated by the ak. …