1998/11/30 by Peter Ozsváth, Zoltán Szabó · 1 citation
Mathematics · #math.DG #math.AG #msc:57 #msc:58
published as Ann. of Math. (2) 151 (2000), no. 1, 93-124 · 32 pages, published version
arxiv created 2000/01/01 · arxiv updated 2009/11/30
In this paper, we demonstrate a relation among Seiberg-Witten invariants which arises from embedded surfaces in four-manifolds whose self-intersection number is negative. These relations, together with Taubes' basic theorems on the Seiberg-Witten invariants of symplectic manifolds, are then used to prove the symplectic Thom conjecture: a symplectic surface in a symplectic four-manifold is genus-minimizing in its homology class. Another corollary of the relations is a general adjunction inequality for embedded surfaces of negative self-intersection in four-manifolds.