In this paper, we derive new adjunction inequalities for embedded surfaces with non-negative self-intersection number in four-manifolds. These formulas are proved by using relations between Seiberg-Witten invariants which are induced from embedded surfaces. To prove these relations, we develop the relevant parts of a Floer theory for four-manifolds which bound circle-bundles over Riemann surfaces.
"Higher Type Adjunction Inequalities in Seiberg-Witten Theory." J. Differential Geom. 55 (3) 385 - 440, July, 2000. https://doi.org/10.4310/jdg/1090341259