  Using the existence of certain symplectic submanifolds in symplectic
4-manifolds, we prove an estimate from above for the number of singular fibers
with separating vanishing cycles in minimal Lefschetz fibrations over surfaces
of positive genus. This estimate is then used to deduce that mapping class
groups are not uniformly perfect, and that the map from their second bounded
cohomology to ordinary cohomology is not injective.
