The symplectic Thom conjecture

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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.

Original languageEnglish (US)
Pages (from-to)93-124
Number of pages32
JournalAnnals of Mathematics
Volume151
Issue number1
DOIs
StatePublished - Jan 2000

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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