Triple points and singularities of projections of smoothly immersed surfaces

Banchoff, Thomas

doi:10.1090/S0002-9939-1974-0377896-X

Triple points and singularities of projections of smoothly immersed surfaces
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Proc. Amer. Math. Soc. 46 (1974), 402-406 Request permission

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.

References

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