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Proceedings of the American Mathematical Society

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Suspending homotopy $ 3$-spheres and embedding mapping cylinders in $ S\sp{4}$


Author: R. C. Lacher
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
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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}$.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0271960-9
Keywords: Suspending homotopy $ 3$-spheres, maps between $ 3$-manifolds, embedding mapping cylinders, $ {S^4}$
Article copyright: © Copyright 1971 American Mathematical Society