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The complement of a codimension-k immersion

Published online by Cambridge University Press:  24 October 2008

Michael D. Hirsch
Michael D. Hirsch
Affiliation:
University of California, Berkeley, CA 94720, U.S.A.
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In [1] Marc Feighn proves the following result: a proper, C2, codimension-1 immersion in a manifold with no first homology separates the ambient space. In [4] Michelangelo Vaccaro proves a related result: the C1-immersed image of a compact n-manifold with image a (curved) polyhedron has non-zero Hn with ℤ2 coefficients. (In Vaccaro's terminology f(M) is a curved polyhedron if f is smooth and f(M) is the (non-PL) embedded image of a simplicial complex.) Using ideas similar to Feighn's we prove here the following result.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 1 , January 1990 , pp. 103 - 107
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

REFERENCES

[1]Feighn, M. E.. Separation properties of codimension-1 immersions. Topology 27 (1988), 319–322.CrossRefGoogle Scholar
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