Louis Funar [1]
Singular fibrations generalize achiral Lefschetz fibrations of
4-manifolds over surfaces
while sharing some of their properties. For instance, relatively minimal
singular fibrations are determined by their monodromy. We explain how to
construct
examples of singular fibrations with a single singularity and
Matsumoto's construction of singular fibrations of the 4-sphere.
Previous results of Hirzebruch and Hopf on 2-plane fields with finitely
many singularities are outlined in connection with the work of Neumann
and Rudolph on the enhanced Milnor number. Eventually, we prove that
closed orientable 4-manifolds with large first Betti number and
vanishing second Betti number do not admit singular fibrations.