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quasar987

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"Show that if M is an oriented manifold,F:M-->N is smooth, and c is a regular values of F, then S:=F

^{-1}(c) is an orientable submanifold of M."

I know that in the case where N=

**R**, then there is a canonical transverse vector field to S given by grad(F), so this determines an orientation on S. But what about the general case? To generalize the above "argument", we would need dim(N) independant vector fields along S (or sections of the normal bundle of S if you prefer) that are transverse to S... where do we find those??