Study on Floer cohomology, mirror symmetry conjecture and singularity

Florer上同调、镜面对称猜想与奇异性研究

基本信息

批准号：
15340020
负责人：
OHTA Hiroshi
金额：
$ 7.1万
依托单位：
Nagoya University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2006
项目状态：
已结题

项目摘要

We revised our paper on obstruction theory and deformation theory of Lagrangian Floer cohomology. This is a joint work with K. Fukaya, Y-G. Oh and K. Ono. In March 2006, we wrote up the manuscript (more than 800 pages) of Chapter 1,2,3,4,5,6,7 and 9 and made the preprint version which were distributed in the world. We established the transversality argument on the spaces with Kuranishi structure. This will play very important role to derive homotopy algebraic structure from various moduli spaces. During the revision, we define the potential function in the context of our-filtered A_∞ algebra and show that it coincides with the super potential of the Landau-Ginzburg model in physics literature. This was predicted by physists Hori and Vafa. In 2006, we have finished to write up the remaining chapters, Chapter 8 and Chapter 10. In Chapter 8, we study the case of semi-positive Lagrangian submanifolds. In this case, we can establish our results over Z or Z_2 coefficients. We apply the results to, for example, the Arnold-Givental conjecture. In Chapter 10, we investigate how the moduli space of pseudo holomorphic discs changes under Lagrangian surgery. We also describe the analytic detail. Moreover, we describe the action of cycles of the ambient symplectic manifold to the filtered A_∞ algebra in terms of L_∞ homomorphism. And we discovered a new relation between the torsion part of our Floer cohomology and Hofer distance of Hamilton isotopy.

我们修订了有关反对理论和拉格朗日浮子共同学的变形理论的论文。这是与K. Fukaya的联合作品，Y-G。哦和K. ono。 2006年3月，我们写了第1,2,3,4,5,6,7和9章的手稿（超过800页），并制作了在世界上分发的预印本版本。我们在具有库兰尼结构的空间上建立了横向论点。这将在从各种模量空间中得出同质代数结构的同性代数结构，将发挥非常重要的作用。在修订过程中，我们在过滤后的A_∞代数的背景下定义了潜在函数，并表明它与物理文献中Landau-Ginzburg模型的超级潜力相吻合。这是由Hori和Vafa物理学预测的。在2006年，我们已经完成了剩余的章节，第8章和第10章。在第8章中，我们研究了半阳性Lagrangian Submanifolds的案例。在这种情况下，我们可以通过z或z_2系数建立结果。我们将结果应用于例如Arnold-Givental概念。在第10章中，我们调查了伪全态光盘的模量如何在拉格朗日手术下变化。我们还描述了分析细节。此外，我们描述了环境符号歧管的循环在滤波的A_∞代数上的循环的作用。我们发现了我们的浮点数的扭转部分与汉密尔顿同位素的Hofer距离之间的新关系。