On the theorems of Sard and de Rham Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/8c97kt30j

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  • A geometric condition on differentiable maps is given which is equivalent to the set of critical values being nowhere dense. In particular, the geometric condition is satisfied for radially ductile maps. On the other hand it is proved that the induced map on the de Rham complex will be a monomorphism, provided the set of regular values is dense. These results, together with Bredon's theorem for ductile maps, yields a generalization of the classical de Rham Theorem.
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