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Embedding piecewise linear manifolds with boundary

Published online by Cambridge University Press:  24 October 2008

C. Mca. Gordon
C. Mca. Gordon
Affiliation:
Florida State University, Tallahassee, Florida, U.S.A.
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Extract

1. Introduction. It is known (6) that the connectivity conditions on the manifolds in Irwin's embedding theorem (7) can be replaced by a connectivity condition on the map. This has led to the suggestion that in Hudson's analogue of Irwin's theorem for bounded manifolds (5), (6), the connectivity conditions on the manifolds modulo boundary can be replaced by the corresponding connectivity condition on the map modulo boundary. The main purpose of the present note is to show that this is in fact false, as is the formal analogue of Irwin's and Hudson's theorems for manifold triads. Its other purpose is to announce a related embedding theorem for manifolds with boundary which appeared in (3).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 1 , July 1972 , pp. 21 - 25
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

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