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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
DOI: https://doi.org/10.1090/S0002-9939-1971-0271919-1
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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Keywords: Three-dimensional manifold, punctured cube, irreducible manifold
Article copyright: © Copyright 1971 American Mathematical Society