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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
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}$.

References [Enhancements On Off] (What's this?)

  • [1] Wolfgang Haken, Some results on surfaces in $ 3$-manifolds, Studies in Modern Topology, Math. Assoc. Amer. (distributed by Prentice-Hall, Englewood Cliffs, N.J.), 1968, pp. 39-98. MR 36 #7118. MR 0224071 (36:7118)
  • [2] W. Heil, On $ {P^2}$-irreducible $ 3$-manifolds, Bull. Amer. Math. Soc. 75 (1969), 772-775. MR 40 #4958. MR 0251731 (40:4958)
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Keywords: $ 3$-manifold, parallelity component, Euler characteristic
Article copyright: © Copyright 1975 American Mathematical Society

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