An elementary proof of a theorem of Izumiya-Marar (Q1384896)
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scientific article; zbMATH DE number 1143507
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An elementary proof of a theorem of Izumiya-Marar |
scientific article; zbMATH DE number 1143507 |
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An elementary proof of a theorem of Izumiya-Marar (English)
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20 April 1998
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The author obtains an elementary and intuitive proof of the following theorem given by \textit{S. Izumiya} and \textit{W. L. Marar} [Mat. Contemp. 5, 53-59 (1993; Zbl 0861.57041)]: Let \(N\) be a closed 2-manifold, \(P\) a 3-manifold and \(f:N\to P\) a smooth stable mapping. Then \[ \chi(f(N))= \chi(N)+ T(f)+ {\textstyle {\frac 12}} C(f), \] where \(T(f)\) is the number of triple points of \(f\) and \(C(f)\) the number of cross-caps.
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0.7585956454277039
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0.7468392252922058
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0.7468392252922058
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