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Two weak Poincaré theorems

Published online by Cambridge University Press:  24 October 2008

P. H. Doylea
P. H. Doylea
Affiliation:
Michigan State University, East Lansing, U.S.A.
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Extract

Theorem 1. Let M3be a compact 3-manifold and let M3 = E3 ∪ R be a standard decomposition where R is a subcomplex in a triangulation of M3((2)). If M3is a homology 3-sphere while R contains no arc that is wild in M3then M3 = S3

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 1 , January 1966 , pp. 23
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

REFERENCES

(1)Bing, R. H.Necessary and sufficient conditions that a 3-manifold be S 3. Ann. of Math. 68 (1958), 17–37.CrossRefGoogle Scholar
(2)Doyle, P. H. and Hocking, J. G.A decomposition theorem for n-dimensional manifolds. Proc. Amer. Math. Soc. 13 (1962), 469–471.Google Scholar
(3)Persinger, C. A. Thesis, Virginia Polytechnic Institute (1964).Google Scholar
(4)Whitehead, J. H. C.Simplicial spaces, nuclei, and m-groups. Proc. London Math. Soc. 45 (1939), 243–327.CrossRefGoogle Scholar