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

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 which are homotopic to bundle maps but which cannot be approximated by bundle maps. Here can be a compact -manifold or some topological -manifold, . The second shows how to construct approximate fibrations whose fibers do not have finite homotopy type, for any of Euler characteristic zero. Here can be a compact -manifold and only has to be an ANR, or can be an -manifold, , and must then also be a topological manifold.

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DOI:
https://doi.org/10.1090/S0002-9947-1983-0688976-3

Keywords:
Approximate fibration,
-manifold,
-manifold

Article copyright:
© Copyright 1983
American Mathematical Society