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 An embedded 2-sphere in irreducible 4-manifolds Bull. Korean Math. Soc. 1999 Vol. 36, No. 4, 683-691 Jongil Park Konkuk University Abstract : It has long been a question which homology class is represented by an embedded $2$-sphere in a smooth $4$-manifold. In this article we study the adjunction inequality, one of main results of Seiberg-Witten theory in smooth $4$-manifolds, for an embedded $2$-sphere. As a result, we give a criterion which homology class cannot be represented by an embedded $2$-sphere in some cases. Keywords : adjunction inequality, smooth $4$-manifold, SW-basic class MSC numbers : 57N13, 57R57 Downloads: Full-text PDF