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Proceedings of the American Mathematical Society

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

 
 

 

Imbedding compact $3$-manifolds in $E^{3}$


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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Keywords: <IMG WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$3$">-manifold, parallelity component, Euler characteristic
Article copyright: © Copyright 1975 American Mathematical Society