Triple points and surgery of immersed surfaces

Banchoff, Thomas F.

doi:10.1090/S0002-9939-1974-0377897-1

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Triple points and surgery of immersed surfaces
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by Thomas F. Banchoff PDF

Proc. Amer. Math. Soc. 46 (1974), 407-413 Request permission

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.

References

Thomas Banchoff, Triple points and singularities of projections of smoothly immersed surfaces, Proc. Amer. Math. Soc. 46 (1974), 402–406. MR 377896, DOI 10.1090/S0002-9939-1974-0377896-X