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Embeddings in Euclidean space

Published online by Cambridge University Press:  24 October 2008

R. L. E. Schwarzenberger
R. L. E. Schwarzenberger
Affiliation:
Department of Pure Mathematics, University of Liverpool
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Extract

Let X be a compact differentiable manifold without boundary. A differentiable regular map of X into Euclidean N-space, dim X < N, is called an immersion (written X £ N). An immersion which is also one-one is called an embedding (written XN). A nonembedding theorem of the form: if X is a manifold with the property P then XN − 1, is best possible if there exists a manifold X with property P and an embedding XN. The purpose of this note is to show that two frequently used non-embedding theorems are best possible.

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 2 , April 1963 , pp. 505 - 507
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

(1)Atiyah, M. F. and Hirzebruch, F.Quelques théorèmes de non-plongement pour les variétés differentiables. Bull. Soc. Math. France, 87 (1959), 383–396.Google Scholar
(2)Epstein, D. B. A. and Schwarzenberger, R. L. E., Imbeddings of real projective spaces. Ann. of Math. 76 (1962), 180–184.CrossRefGoogle Scholar
(3)Massey, W. S., On the Stiefel-Whitney classes of a manifold. Amer. J. Math. 82 (1960), 92–102.CrossRefGoogle Scholar
(4)Sanderson, B. J., Immersions and embeddings of projective spaces. Proc. London Math. Soc. (in the press).Google Scholar