Tamed to compatible: symplectic forms via moduli space integration
Tamed to compatible: symplectic forms via moduli space integration
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DOI：
10.4310/jsg.2011.v9.n2.a4
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发表时间：
2009-10
影响因子：
0.7
通讯作者：
C. Taubes
中科院分区：
文献类型：
--
作者：
C. Taubes
固定一个紧的四维流形，其自对偶第二贝蒂数为1，并具有给定的辛形式。本文证明了：由给定的辛形式定义的驯服的几乎复结构的Frechet空间有一个开的稠密子集，其复结构关于与给定的辛形式上同调的辛形式是相容的。通过在由伪全纯曲线定义的电流空间上积分，构造新的辛形式，证明了该定理。
Fix a compact 4-dimensional manifold with self-dual 2nd Betti number one and with a given symplectic form. This article proves the following: The Frechet space of tamed almost complex structures as defined by the given symplectic form has an open and dense subset whose complex structures are compatible with respect to a symplectic form that is cohomologous to the given one. The theorem is proved by constructing the new symplectic form by integrating over a space of currents that are defined by pseudo-holomorphic curves.