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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Manifolds with finite first homology as codimension $ 2$ fibrators


Author: Robert J. Daverman
Journal: Proc. Amer. Math. Soc. 113 (1991), 471-477
MSC: Primary 55R65; Secondary 54B15, 57M25, 57N12, 57N15, 57N65
MathSciNet review: 1086581
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Abstract: Given a map $ f:M \to B$ defined on an orientable $ (n + 2)$-manifold with all point inverses having the homotopy type of a specified closed $ n$-manifold $ N$, we seek to catalog the manifolds $ N$ for which $ f$ is always an approximate fibration. Assuming $ {H_1}(N)$ finite, we deduce that the cohomology sheaf of $ f$ is locally constant provided $ N$ admits no self-map of degree $ d > 1$ when $ {H_1}(N)$ has a cyclic subgroup of order $ d$. For manifolds $ N$ possessing additional features, we achieve the approximate fibration conclusion.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1086581-0
PII: S 0002-9939(1991)1086581-0
Keywords: Approximate fibration, approximate lifting, continuity set, codimension 2 fibrator, geometric structure, Hopfain group, mapping degree
Article copyright: © Copyright 1991 American Mathematical Society