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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A characterisation of punctured open $ 3$-cells


Authors: O. L. Costich, P. H. Doyle and D. E. Galewski
Journal: Proc. Amer. Math. Soc. 28 (1971), 295-298
MSC: Primary 54.78
MathSciNet review: 0271919
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Abstract: A proof is given using standard methods of the topology of three-dimensional manifolds of the following characterization of punctured cubes: A connected, open $ 3$-manifold $ M$ is topological $ {E^3}$ with $ k$ points removed if and only if every polyhedral simple closed curve in $ M$ lies in a topological cube in $ M$ and the rank of $ {\pi _2}(M)$ is $ k$. An application is given.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0271919-1
PII: S 0002-9939(1971)0271919-1
Keywords: Three-dimensional manifold, punctured cube, irreducible manifold
Article copyright: © Copyright 1971 American Mathematical Society