Symplectic structure on ruled surfaces and a generalized adjunction formula

Abstract

In this section, we state the theorems needed in our paper. Recently, Seiberg and Witten ([SW], [Wi]) have introduced a new set of 4-manifold invariants. These invariants are in similar spirit to Donaldson invariants but much easier to handle. Various longstanding conjectures including the Thom conjecture are proved using Seiberg-Witten invariants. An important ingredient in the proof of the Thom conjecture by Kronheimer and Mrowka is the wall crossing formula for manifolds with b 1 = 0.