Immersed |
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Authors: | Osamu Saeki Kazuhiro Sakuma |
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Affiliation: | Department of Mathematics, Faculty of Science, Hiroshima University, Higashi-Hiroshima 739, Japan ; Department of General Education, Kochi National College of Technology, Nankoku City, Kochi 783, Japan |
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Abstract: | We give two congruence formulas concerning the number of non-trivial double point circles and arcs of a smooth map with generic singularities --- the Whitney umbrellas --- of an -manifold into , which generalize the formulas by Szücs for an immersion with normal crossings. Then they are applied to give a new geometric proof of the congruence formula due to Mahowald and Lannes concerning the normal Euler number of an immersed -manifold in . We also study generic projections of an embedded -manifold in into and prove an elimination theorem of Whitney umbrella points of opposite signs, which is a direct generalization of a recent result of Carter and Saito concerning embedded surfaces in . The problem of lifting a map into to an embedding into is also studied. |
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Keywords: | Double point circle Whitney umbrella normal Euler number generic projection |
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