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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Triple points and surgery of immersed surfaces


Author: Thomas F. Banchoff
Journal: Proc. Amer. Math. Soc. 46 (1974), 407-413
MSC: Primary 57A35; Secondary 57D45, 57D40
MathSciNet review: 0377897
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Abstract: For a sufficiently general immersion of a smooth or polyhedral 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 involves elementary notions of modification of surfaces by surgery.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0377897-1
PII: S 0002-9939(1974)0377897-1
Keywords: Triple points, surgery, immersions, Euler characteristic
Article copyright: © Copyright 1974 American Mathematical Society