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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
DOI: https://doi.org/10.1090/S0002-9939-1974-0377896-X
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.


References [Enhancements On Off] (What's this?)

  • [1] T. F. Banchoff, Critical points and curvature for embedded polyhedral surfaces, Amer. Math. Monthly 77 (1970), 475-485. MR 41 #4444. MR 0259812 (41:4444)
  • [2] -, Stiefel Whitney homology classes and singularities of projections for polyhedral manifolds, Proc. Sympos. Pure Math., vol. 27, Amer. Math. Soc., Providence, R. I., 1975 (to appear). MR 0377921 (51:14090)
  • [3] -, Triple points and surgery of immersed surfaces, Proc. Amer. Math. Soc. 46 (1974), 407-413. MR 0377897 (51:14066)
  • [4] R. K. Lashof and S. Smale, Self-intersections of immersed manifolds, J. Math. Mech. 8 (1959), 143-157. MR 21 #332. MR 0101522 (21:332)
  • [5] J. White, Twist invariants and Pontrjagin classes of immersed manifolds, Proc. Sympos. Pure Math., vol. 27, Amer. Math. Soc., Providence, R. I., 1975 (to appear). MR 0405455 (53:9248)

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Additional Information

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

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