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Constructing approximate fibrations


Authors: T. A. Chapman and Steve Ferry
Journal: Trans. Amer. Math. Soc. 276 (1983), 757-774
MSC: Primary 55R65; Secondary 57N15, 57N30
DOI: https://doi.org/10.1090/S0002-9947-1983-0688976-3
MathSciNet review: 688976
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Abstract: In this paper two results concerning the construction of approximate fibrations are established. The first shows that there are approximate fibrations $ p:M \to S^2$ which are homotopic to bundle maps but which cannot be approximated by bundle maps. Here $ M$ can be a compact $ Q$-manifold or some topological $ n$-manifold, $ n \geqslant 5$. The second shows how to construct approximate fibrations $ p:M \to B$ whose fibers do not have finite homotopy type, for any $ B$ of Euler characteristic zero. Here $ M$ can be a compact $ Q$-manifold and $ B$ only has to be an ANR, or $ M$ can be an $ n$-manifold, $ n \geqslant 6$, and $ B$ must then also be a topological manifold.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0688976-3
Keywords: Approximate fibration, $ n$-manifold, $ Q$-manifold
Article copyright: © Copyright 1983 American Mathematical Society

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