Louis Funar

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.