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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Imbedding compact $3$-manifolds in $E^{3}$
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by Tom Knoblauch PDF
Proc. Amer. Math. Soc. 48 (1975), 447-453 Request permission

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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Additional Information
  • © Copyright 1975 American Mathematical Society
  • 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