Categorical Algebra and Topological Field Theory

分类代数和拓扑场论

基本信息

批准号：
07640111
负责人：
FUKAYA Kenji
金额：
$ 1.6万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07640111/
关键词：
Topological Field Theory Hamiltonian system Gauge theory Sympletic geometry Morse theory String Theory Homotopical Algebra Whitehead Torsion 超弦理論有理ホモトピー型概複素曲線周期軌道

项目摘要

We studied morse homotopy theory of higher genus and find that it coicides with Chern-Simons Perturbation theory.We are tring to quantize S cobordism theorem, which is an important application of algebraic K-theory to topology. We find a version of Whitehead Torsion in Floer homology. As an application we find an example of a pair of Lalangina submanifold such has a trivial Floer homology (of Lagrangian intersection) but can not be made disjoint by Hamiltonian diffeomorphism.Fukaya and Ono proved a homology version of Arnold conjecture on the number of periodic orbit of Hamiltonian system.Fukaya and Ono constructed Gromov-Witten invariant for general syjmplectic manifolds.Fukaya and Oh studied pseudo holomorphic disks in cotangent bundles with Lagrangian boundary condition and find that it is equivalent to the rational homotopy theory on the base.We studied homological algebra of A infinity category and proved a version of Yoneda's Lemma.This homological algebra has a geometrid application, to the definition of the Foer homology of 3 manifolds with boundary and construction of an A infinity category associated to an Symplectic manifolds, (using Lagrangian submanifolds.)Fukaya completed a paper including anouncement of them and the full detail of the proof of homolomocai algebra part.One need analysis of nonlinear PDE for geometric application. Fukaya wrote a paper describing a main part of it and is preparing papers describing the full detail of Analysis.

我们研究了高等属的莫尔斯同伦理论，发现它与Chern-Simons微扰理论相吻合。我们正在尝试量子化S配边定理，这是代数K理论在拓扑学上的一个重要应用。我们在弗洛尔同调中找到了怀特海扭转的一个版本。作为一个应用，我们找到了一对 Lalangina 子流形的例子，它具有微不足道的弗洛尔同调（拉格朗日交集），但不能通过哈密顿微分同胚使其不相交。Fukaya 和 Ono 证明了关于周期轨道数的阿诺德猜想的同调版本Fukaya 和 Ono 构造了一般辛流形的 Gromov-Witten 不变量。Fukaya 和 Oh 研究了伪我们研究了具有拉格朗日边界条件的余切丛中的全纯圆，发现它等价于基上的有理同伦理论。我们研究了 A 无穷范畴的同调代数，并证明了米田引理的一个版本。这个同调代数有一个几何应用，到定义具有边界的 3 个流形的 Foer 同调性以及与辛流形相关的 A 无穷范畴的构造，（使用拉格朗日子流形。）Fukaya 完成了一篇论文，包括它们的公布以及同形代数部分证明的全部细节。几何应用需要分析非线性偏微分方程。 Fukaya 写了一篇论文描述了它的主要部分，并且正在准备描述分析的全部细节的论文。