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 ${M^3}$.References
- Wolfgang Haken, Some results on surfaces in $3$-manifolds, Studies in Modern Topology, Math. Assoc. America, Buffalo, N.Y.; distributed by Prentice-Hall, Englewood Cliffs, N.J., 1968, pp.Β 39β98. MR 0224071
- Wolfgang Heil, On $P^{2}$-irreducible $3$-manifolds, Bull. Amer. Math. Soc. 75 (1969), 772β775. MR 251731, DOI 10.1090/S0002-9904-1969-12283-4 H. Seifert and W. Threlfall, Lehrbuch der Topologie, Teubner, Leipzig, 1934; reprint, Chelsea, New York, 1947.
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