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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Imbedding compact $ 3$-manifolds in $ E\sp{3}$


Author: Tom Knoblauch
Journal: Proc. Amer. Math. Soc. 48 (1975), 447-453
MSC: Primary 57A10
DOI: https://doi.org/10.1090/S0002-9939-1975-0368010-6
MathSciNet review: 0368010
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Abstract: We show that in a large finite disjoint collection of compacta in a closed orientable $ 3$-manifold there is a compactum that imbeds in $ {E^3}$. However, given a closed $ 3$-manifold $ {M^3}$, there is a pair of compact $ 3$-manifolds $ (L,N)$ such that $ L$ contains infinitely many disjoint copies of $ N$ but $ N$ does not imbed in $ {M^3}$.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0368010-6
Keywords: $ 3$-manifold, parallelity component, Euler characteristic
Article copyright: © Copyright 1975 American Mathematical Society