On transversality with deficiency and a conjecture of Sard |
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Authors: | Carlos Biasi Osamu Saeki |
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Affiliation: | Departamento de Matemática, ICMSC-USP, Caixa Postal 668, 13560-970, São Carlos, SP, Brazil ; Department of Mathematics, Faculty of Science, Hiroshima University, Higashi- Hiroshima 739, Japan |
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Abstract: | Let be a map between manifolds and a manifold. In this paper, by using the Sard theorem, we study the topological properties of the space of maps which satisfy a certain transversality condition with respect to in a weak sense. As an application, by considering the case where is a point, we obtain some new results about the topological properties of , where is the set of points of where the rank of the differential of is less than or equal to . In particular, we show a result about the topological dimension of , which is closely related to a conjecture of Sard concerning the Hausdorff measure of . |
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Keywords: | |
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