Fibrations over aspherical manifolds

Daciberg Gonçalves and Peter Wong

Let f: E → B be a map between closed connected orientable manifolds. In this note, we give a necessary condition for f to be a manifold fibration. In particular, we show that if f: E → B is a fibration where F=f⁻¹(b), E and B are closed connected triangulated orientable manifolds and B is aspherical, then f|_E⁽ⁿ⁾: E⁽ⁿ⁾ → B is surjective, where E⁽ⁿ⁾ denotes the n-th skeleton of E and n=dimB.

Homology, Homotopy and Applications, Vol. 8 (2006), No. 1, pp.257-261.

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