Constraints on Basic Classes of Lefschetz Fibrations

Minimal general type complex surfaces are known to have very simple Seiberg-Witten invariants, whereas the Ozsvath-Szabo invariants of symplectic 4-manifolds can have more varied behavior. The thesis provides a geometric-topological condition on a symplectic 4-manifold, namely containing some particular piece as Lefscehtz subfibration, which guarantees that the Ozsvath-Szabo invariant of the symplectic 4-manifold behaves the same way as the Seiberg-Witten invariants of minimal general type complex surfaces.