Manifolds with finite first homology as codimension 2 fibrators

Daverman, Robert J.

doi:10.1090/S0002-9939-1991-1086581-0

Manifolds with finite first homology as codimension $2$ fibrators
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Proc. Amer. Math. Soc. 113 (1991), 471-477 Request permission

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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