Classes of obstruction to multi-transversality of smooth mappings

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1974

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This thesis represents an attempt to apply Algebraic Topology methods to study singularities of smooth mappings in the sense of Thom-Mather. The Thom-Haefliger and Wu-Bourgin classes are extended to multi-jet bundles and reduced-jet spaces. These extensions are related by the first main result of this thesis. It is shown that the classes of multi-jets and the classes of reduced-jets are classes of obstruction to multi-transversality. As an application, Mather results on C[infinity] stability are obtained in the multi-jet case and Thom results on homotopic stability are obtained in the reduced-jet case.

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