Moduli space and infinite dimensional geometry

模空间和无限维几何

基本信息

批准号：
09304008
负责人：
FUKAYA Kenji
金额：
$ 17.92万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A).
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 2000
项目状态：
已结题

项目摘要

Fukaya, Ono, Ohta together with Oh constructed an obstruction theory for Lagrangian intersection Floer homology to be well defined. Based on it, an (algebraic) deformation theory of Lagrangian submanifold and quantum deformation of Lagrangian submanifold is constructed. We finished a preliminary version of the book (of 350 pages) describing them in Dec. 2000. After than we made a progress on homotopical algebra part and clarify the relation to classical homotopy type etc. So we are now adding more material (approximately 100 pages).Our Lagrangian intersection Floer theory is an open string version of the theory of Gromov-Witten invariant which are completed by several mathematicians including Fukaya-Ono.In our case of open string version, we need more careful treatment on homological algebra part for example so that we need to develop homotopical algebra itself for this purpose.The orientation of the moduli space is also a delicate question since the moduli space of pseudoholomorphic d … More isks do not carry an almost complex structure. Moreover we need additional argument to work out analytic detail mainly because we need to work in the chain level.While working out the detail of the Lagrangian intersection Floer theory, we have a better understanding of the relation between quantum field theory and various notions developed in the late half of the 20 th century. For example we observed a close relation between Feynman diagram, homotopical algebra and of local deformation theory.Nakajima pursuit his study to construct interesting algebraic structures based on moduli spaces. In his study, various example which are supposed to play the central role in the theory is studied in detail explicitly and various interesting new algebraic structures are constructed.Furuta and his coauthors further studied a relation between moduli space in 4 dimensional gauge theory and stable homotopy theory. This point of view is already appeared in Furuta's proof of 10/8 theorem of intersection form of 4 manifolds. By recent development, several interesting applications such as construction of new invariant of homology 3 spheres and study of embedding of surface in the connected sum of two K3 surfaces. are obtained.f embedding of surface in the Less

OHTA的福卡亚（Fukaya），OH与OH一起构建了一个反对理论，该理论定义了Lagrangian交叉点浮点同源性。基于它，构建了拉格朗日亚法德的（代数）变形理论和拉格朗日亚曼氏的量子变形。 We finished a preliminary version of the book (of 350 pages) describing them in Dec. 2000. After we made a progress on homotopical algebra part and clarify the relationship to classic homotopy type etc. So we are now adding more material (approximately 100 pages).Our Lagrangian intersection Floer theory is an open string version of the theory of Gromov-Witten invariant which are completed by several mathematicians including Fukaya-Ono.In我们的开放字符串版本的情况是，我们需要对同源代数部分进行更仔细的处理，以便为此目的开发同位代数本身。模量空间的方向也是一个微妙的问题，因为伪酚晶的模量空间……更多的isks不会带有几乎复杂的结构。此外，我们需要其他参数来解决分析细节，主要是因为我们需要在链级上工作。在研究拉格朗日交叉路口理论的细节时，我们对量子场理论与20世纪末期开发的各种说明之间的关系有了更好的了解。例如，我们观察到Feynman图，同源代数和局部变形理论之间存在密切的关系。Nakajima追求他的研究，以建造基于模量空间的有趣代数结构。在他的研究中，明确研究了应该在理论中发挥核心作用的各种示例，并构建了各种有趣的新代数结构。FURUTA及其合着者进一步研究了4维仪表理论中模量空间之间的关系。这种观点已经出现在Furuta证明4个歧管的交叉形式的10/8定理的证明中。根据最近的开发，几种有趣的应用，例如同源3球的新不变型的构建以及在两个K3表面的连接总和中对表面嵌入的研究。获得表面嵌入在较少的