The symplectic Thom conjecture

Details The symplectic Thom conjecture The symplectic Thom conjecture

1998-11-13

arxiv.org/abs/math/9811087v2

Ann. of Math. (2) 151 (2000), no. 1, 93-124

Mathematics

Differential Geometry

32 pages, published version

Scientific paper

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.

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