闭伪全纯曲线的无分支覆盖的通有横截性
Generic transversality for unbranched covers of closed pseudoholomorphic curves
摘要：
我们证明了在任意维的闭殆复流形中，殆复结构的一般扰动足以使变形指数为零的简单伪全纯曲线的所有无分支多重覆盖达到横截性.一个推论是，辛4-流形的Gromov-Witten不变量（没有后代）总是可以计算为一般驯服J的诚实J-全纯曲线的带符号和加权计数：特别地，每个这样的不变量是一个整数除以一个权重因子，该因子仅取决于对应的同调类的可分性。横截性的证明是基于一个分析扰动技术，最初是由于Taubes。
英文摘要：
We prove that in closed almost complex manifolds of any dimension, generic perturbations of the almost complex structure suffice to achieve transversality for all unbranched multiple covers of simple pseudoholomorphic curves with deformation index zero. A corollary is that the Gromov-Witten invariants (without descendants) of symplectic 4-manifolds can always be computed as a signed and weighted count of honest J-holomorphic curves for generic tame J: in particular, each such invariant is an integer divided by a weighting factor that depends only on the divisibility of the corresponding homology class. The transversality proof is based on an analytic perturbation technique, originally due to Taubes.
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