We show that there are homeomorphisms of closed oriented genus surfaces which are fiber-preserving with respect to an irregular branched covering and isotopic to the identity, but which are not fiber-isotopic to the identity.

We show that any 4-manifold, after surgery on a curve, admits an achiral Lefschetz fibration. In particular, if X is a simply connected 4-manifold we show that X#S 2 × S 2 and X#S 2×eS 2 both admit achiral Lefschetz fibrations. We also show these surg . . .

Let M be a smooth 4-manifold which admits a relatively minimal hyperelliptic genus h Lefschetz fibration over S2. If all of the vanishing cycles for this fibration are nonseparating curves, then we show that M is a 2-fold cover of an S2-bundle over S2 . . .