Suspending homotopy $3$-spheres and embedding mapping cylinders in $S^{4}$
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- by R. C. Lacher
- Proc. Amer. Math. Soc. 27 (1971), 584-586
- DOI: https://doi.org/10.1090/S0002-9939-1971-0271960-9
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Abstract:
A property of maps between closed $3$-manifolds, implied by cellularity and implying $U{V^\infty }$, is that the mapping cylinder embed locally in ${S^4}$. It is not clear what topological properties are preserved under such maps. In the present note, we show that a closed $3$-manifold admits such a map onto ${S^3}$ if and only if its suspension is ${S^4}$.References
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Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 584-586
- MSC: Primary 57.05
- DOI: https://doi.org/10.1090/S0002-9939-1971-0271960-9
- MathSciNet review: 0271960