an:04201147
Zbl 0727.55009
Daverman, Robert J.
Manifolds with finite first homology as codimension 2 fibrators
EN
Proc. Am. Math. Soc. 113, No. 2, 471-477 (1991).
00157238
1991
j
55R65 57N15 57N65
orientable manifold; homotopy type; approximate fibration; cohomology sheaf
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.