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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Bundle theories for topological manifolds


Authors: C. B. Hughes, L. R. Taylor and E. B. Williams
Journal: Trans. Amer. Math. Soc. 319 (1990), 1-65
MSC: Primary 57N55; Secondary 55R10, 55R35
MathSciNet review: 1010410
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Abstract: Manifold approximate fibrations arise in the geometric topology of manifolds and group actions on topological manifolds. The primary purpose of this paper is to classify manifold approximate fibrations in terms of the lifting problem for a certain bundle. Our classification meshes well with the classical classifications of fibrations and bundles and, hence, we are able to attack questions such as the following. When is a fibration controlled homotopy equivalent to a manifold approximate fibration? When is a manifold approximate fibration controlled homeomorphic to a bundle?


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-1010410-8
PII: S 0002-9947(1990)1010410-8
Keywords: Manifold approximate fibration, fibration, bundle, controlled structures
Article copyright: © Copyright 1990 American Mathematical Society