Seiberg{Witten Invariants and Pseudo-Holomorphic Subvarieties for Self-Dual, Harmonic 2{Forms
Seiberg{Witten Invariants and Pseudo-Holomorphic Subvarieties for Self-Dual, Harmonic 2{Forms
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Seiberg{Witten 不变量和自对偶、调和 2{形式的伪全纯子簇
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发表时间：
1999
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影响因子：
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通讯作者：
C. Taubes
中科院分区：
文献类型：
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作者：
C. Taubes
具有黎曼度量且b2+1h为非平凡的、闭的、自对偶的2{形式的光滑、紧致的4{流形。如果度量是一般的，则这种形式的零集是不相交的圆的并。在这个零集的补集上，辛型和度规是一个几乎复杂的结构，后者可以用于Dene伪全纯子流形和子簇。本文的主要定理是：如果4{流形具有非零的Seiberg{Witten不变量，则任何给定的自对偶调和2{形式的零集是其补中的伪全纯子簇的边界。
A smooth, compact 4{manifold with a Riemannian metric and b 2+ 1h as a non-trivial, closed, self-dual 2{form. If the metric is generic, then the zero set of this form is a disjoint union of circles. On the complement of this zero set, the symplectic form and the metric dene an almost complex structure; and the latter can be used to dene pseudo-holomorphic submanifolds and subvarieties. The main theorem in this paper asserts that if the 4{manifold has a non zero Seiberg{Witten invariant, then the zero set of any given self-dual harmonic 2{form is the boundary of a pseudo-holomorphic subvariety in its complement.