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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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