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The symplectic Thom conjecture

Peter Ozsváth·Zoltán Szabó
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Abstract

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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Peter Ozsváth, Zoltán Szabó. 2000-01-01. The symplectic Thom conjecture. https://arxiv.org/abs/math/9811087

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