Lagrangian Intersection Floer Theory, Part 2: Anomaly and Obstruction, Part II
Lagrangian Intersection Floer Theory, Part 2: Anomaly and Obstruction, Part II
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拉格朗日交集弗洛尔理论，第 2 部分：异常和障碍，第 II 部分
DOI：
10.1090/amsip/046.2
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
K. Ôno
中科院分区：
文献类型：
--
作者：
K. Fukaya;Y. Oh;H. Ohta;K. Ôno
这是一本关于一般拉格朗日Floer理论和伴随的滤子代数的同调代数的两卷系列研究专著。这本书提供了最重要的一步，在一般情况下为福屋范畴奠定了严格的基础。在第一卷中，Floer上同调的一般形变理论在代数和几何两个方面都得到了发展。给出了滤子代数和双模的本质自包含同伦理论及其阻塞变形理论在拉格朗日Floer理论中的应用。第二卷详细研究了该理论基础的两个主要观点：横向性和方向性。横断性的研究是基于虚拟基本链技术(仓西结构及其多节理论)和链级相交理论。对模空间及其纤维产物的取向进行了详细的分析比较。本卷的附录中还包括了仓西结构的一般理论的完整叙述。
This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filteredalgebras andbimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-contained account of the general theory of Kuranishi structures is also included in the appendix of this volume.