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Manifolds with finite first homology as codimension 2 fibrators. (English) Zbl 0727.55009
Summary: 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.

MSC:
55R65 Generalizations of fiber spaces and bundles in algebraic topology
57N15 Topology of the Euclidean \(n\)-space, \(n\)-manifolds (\(4 \leq n \leq \infty\)) (MSC2010)
57N65 Algebraic topology of manifolds
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