The polyfold--Kuranishi correspondence I: A choice-independent theory of Kuranishi structures
The polyfold--Kuranishi correspondence I: A choice-independent theory of Kuranishi structures
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多重折叠--Kuranishi对应I：Kuranishi结构的选择无关理论
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Dingyu Yang
中科院分区：
文献类型：
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作者：
Dingyu Yang
这是第一个文件中的一系列提出和发展的polyfold Fredholm结构-Kuranishi结构对应，确定这两个抽象的扰动结构是必不可少的建设和理解辛不变量在最一般的设置。在本文中，我提出了我的版本的仓西结构的理论在充分的一般性。这个理论独立于在构造中所做的所有选择（包括好的坐标系的选择）;它使用仓西结构的等价性作为萌芽，以捕捉微扰理论所下降到的内在基础结构。这是文献中第一个具有这两个性质的理论。这种选择独立的理论是必不可少的规范和功能性识别的多重Fredholm理论的霍费尔-Wysocki-Zehnder与理论的Kuranishi结构。本系列的下两篇论文将分别讨论多重-仓西对应中的遗忘函子和全球化函子，并通过一些示例应用说明对应的使用。
This is the first paper in a series which proposes and develops the polyfold Fredholm structure--Kuranishi structure correspondence, identifying these two abstract perturbative structures which are indispensable for constructing and understanding symplectic invariants in the most general settings. In this paper, I present my version of the theory of Kuranishi structures in full generality. This theory is independent of all the choices made in the construction (including the choices of good coordinate systems); and it uses the equivalence of Kuranishi structures as the germ to capture the intrinsic underlying structure to which the perturbation theory descends. This is the first theory in the literature that has these two properties. This choice-independent theory is essential for canonically and functorially identifying the polyfold Fredholm theory of Hofer-Wysocki-Zehnder with the theory of Kuranishi structures. The next two papers in this series will be on the forgetful functor and the globalization functor in the respective directions of the polyfold--Kuranishi correspondence, as well as illustrating the use of the correspondence with a few sample applications.