The symplectic Thom conjecture
Differential Geometry
2007-05-23 v2 Algebraic Geometry
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.
Cite
@article{arxiv.math/9811087,
title = {The symplectic Thom conjecture},
author = {Peter Ozsváth and Zoltán Szabó},
journal= {arXiv preprint arXiv:math/9811087},
year = {2007}
}
Comments
32 pages, published version