Constructing approximate fibrations

Chapman, T. A.; Ferry, Steve

doi:10.1090/S0002-9947-1983-0688976-3

Constructing approximate fibrations
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by T. A. Chapman and Steve Ferry PDF

Trans. Amer. Math. Soc. 276 (1983), 757-774 Request permission

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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