Texts: 1. For smooth manifolds M, N, and a smooth map f: M → N, define the notions of a) critical value and b) rank 2. 2. Prove Sard's Theorem in the one-dimensional case.
Added by Kristine G.
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A critical value of f is a point y in the target manifold N such that there exists a point x in the domain manifold M where the differential of f at x, denoted by df_x, is not surjective. In other words, the rank of df_x is less than the dimension of N. Show more…
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