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Annals of Mathematics, II. Series Vol. 151, No. 1, pp. 93124 (2000) 

The symplectic Thom conjecturePeter Ozsváth and Zoltán SzabóReview from Zentralblatt MATH: In this paper, the authors prove the symplectic Thom conjecture in its full generality: Theorem. An embedded symplectic surface in a closed, symplectic fourmanifold is genusminimizing in its homology class. As a corollary, they also get the following result in the Kähler case. Corollary. An embedded holomorphic curve in a Kähler surface is genusminimizing in its homology class. The theorem follows from a relation among SeibergWitten invariants, that holds in the case of embedded surfaces in fourmanifolds whose selfintersection number is negative. Such a relation also yields a general adjunction inequality for embedded surface of negative selfintersection in fourmanifolds. Reviewed by Alberto Parmeggiani Keywords: symplectic manifold; Spin$_{\Bbb C}$ structure; SeibergWitten invariants; symplectic Thom conjecture Classification (MSC2000): 53D35 57R57 53C55 Full text of the article:
Electronic fulltext finalized on: 8 Sep 2001. This page was last modified: 21 Jan 2002.
© 2001 Johns Hopkins University Press
