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Non-immersion theorems for differentiable manifolds

Published online by Cambridge University Press:  24 October 2008

B. J. Sanderson  and
R. L. E. Schwarzenberger
B. J. Sanderson
Affiliation:
Department of Pure Mathematics, University of Liverpool
R. L. E. Schwarzenberger
Affiliation:
Department of Pure Mathematics, University of Liverpool
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Extract

Let X be a compact differentiable n-manifold of class C∞ and let f be a C∞ map of X into euclidean (n + k)-space. Then f is an immersion if its jacobian has rank n at each point of X. It is an embedding if it is also one-one. We write X ⊆ n + k to denote the existence of an immersion, X ⊂ n + k to denote the existence of an embedding. By a theorem of Whitney, we have X ⊆ 2n − 1, X ⊂ 2n.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 2 , April 1963 , pp. 319 - 322
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

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