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An elementary proof of the classification of surfaces in the projective $ 3$-space

Author: J. H. C. Creighton
Journal: Proc. Amer. Math. Soc. 72 (1978), 191-192
MSC: Primary 54D40
MathSciNet review: 0515780
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Abstract: A closed surface embeds in the 3-dimensional real projective space if and only if it is orientable or of odd Euler characteristic. The proof given is elementary in the sense that only geometric techniques are used.

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

  • [1] G. E. Bredon and J. W. Wood, Non-orientable surfaces in orientable 3-manifolds, Invent. Math. 7 (1969), 83-110. MR 0246312 (39:7616)
  • [2] J. H. C. Creighton, Hypersurfaces in lens spaces (to appear).
  • [3] E. Stiefel, Richtungsfelder und Fernparallelismus in n-dimensionalen Mannigfaltigkeiten (Anhang I, §2), Comment. Math. Helv. 8 (1935), 305-353. MR 1509530

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Keywords: Real projective 3-space, surgery
Article copyright: © Copyright 1978 American Mathematical Society

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