二维半简单域论的结构
The structure of 2D semi-simple field theories
摘要：
基于半单复Frobenius代数A对所有上同调二维域论进行了分类。它们由卡帕类的线性组合和Deligne-Mumford边界的扩展基准面控制。它们对Gromov-Witten势的影响由Givental的Fock空间公式描述。这导致重建的Gromov-Witten不变量从量子杯积在一个单一的半单点和从第一陈类，证实了Givental的高亏格重建猜想。证明使用了Madsen和Weiss证明的Mumford猜想。
英文摘要：
I classify all cohomological 2D field theories based on a semi-simple complex Frobenius algebra A. They are controlled by a linear combination of kappa-classes and by an extension datum to the Deligne-Mumford boundary. Their effect on the Gromov-Witten potential is described by Givental's Fock space formulae. This leads to the reconstruction of Gromov-Witten invariants from the quantum cup-product at a single semi-simple point and from the first Chern class, confirming Givental's higher-genus reconstruction conjecture. The proof uses the Mumford conjecture proved by Madsen and Weiss.
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