An elementary proof of the classification of surfaces in the projective 
-space
Author:
J. H. C. Creighton
Journal:
Proc. Amer. Math. Soc. 72 (1978), 191-192
MSC:
Primary 54D40
DOI:
https://doi.org/10.1090/S0002-9939-1978-0515780-2
MathSciNet review:
0515780
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Abstract | References | Similar Articles | Additional Information
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.
- [1] Glen E. Bredon and John W. Wood, Non-orientable surfaces in orientable 3-manifolds, Invent. Math. 7 (1969), 83–110. MR 0246312, https://doi.org/10.1007/BF01389793
- [2] J. H. C. Creighton, Hypersurfaces in lens spaces (to appear).
- [3] E. Stiefel, Richtungsfelder und Fernparallelismus in n-dimensionalen Mannigfaltigkeiten, Comment. Math. Helv. 8 (1935), no. 1, 305–353 (German). MR 1509530, https://doi.org/10.1007/BF01199559
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1978-0515780-2
Keywords:
Real projective 3-space,
surgery
Article copyright:
© Copyright 1978
American Mathematical Society
