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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Triple points and singularities of projections of smoothly immersed surfaces


Author: Thomas Banchoff
Journal: Proc. Amer. Math. Soc. 46 (1974), 402-406
MSC: Primary 57A35; Secondary 57D45, 57D40
MathSciNet review: 0377896
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Abstract: For a transversal smooth immersion of a closed $ 2$-dimensional surface into Euclidean $ 3$-space, the number of triple points is congruent modulo 2 to the Euler characteristic. The approach of this paper includes an introduction to normal Euler classes of smoothly immersed manifolds by means of singularities of projections.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0377896-X
Keywords: Triple points, singularities of projections, immersions, Euler characteristic
Article copyright: © Copyright 1974 American Mathematical Society