Airy structures and symplectic geometry of topological recursion
Airy structures and symplectic geometry of
topological recursion
复制标题
艾里结构和拓扑递归的辛几何
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Y. Soibelman
中科院分区：
文献类型：
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作者：
M. Kontsevich;Y. Soibelman
本文基于Airy结构的概念，提出了一种新的Eynard-Orantin拓扑递归方法。我们解释了为什么艾里结构是一个更基本的对象比光谱曲线之一。我们解释了艾里结构的量子化概念如何自然地导出拓扑递归公式及其推广。谱曲线的概念也被认为是在一个更一般的框架泊松表面赋予叶理。我们解释了谱曲线的变形理论如何与艾里结构相关。其他一些问题（如全纯异常方程）也从艾里结构的一般观点进行了讨论。
We propose a new approach to the topological recursion of Eynard-Orantin based on the notion of Airy structure, which we introduce in the paper. We explain why Airy structure is a more fundamental object than the one of the spectral curve. We explain how the concept of quantization of Airy structure leads naturally to the formulas of topological recursion as well as their generalizations. The notion of spectral curve is also considered in a more general framework of Poisson surfaces endowed with foliation. We explain how the deformation theory of spectral curves is related to Airy structures. Few other topics (e.g. the Holomorphic Anomaly Equation) are also discussed from the general point of view of Airy structures.