Topologs of manifolds and mathematical plysics

流形拓扑和数学物理

• 批准号: 05640105
• 负责人: KONO Akira
• 金额: $ 1.28万
• 依托单位: KYOTO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1993
• 资助国家: 日本
• 起止时间: 1993 至 1994
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-05640105/
• 关键词: free loop space; K-theor; Moise function; Morse homotopy; Quantun homotopy type; conformal field thery; vector bmdle; 自由ループ室間; 楕円コホモロジー; モジュライ室間; Mose函数; 自由ループ群; 分類空間; モジュライ空間; 代数ベクトル束; 量子群

The reserch results supported by Grants in Aid for Scientific Reserch (C) 05640105 consist of the following1. Free loop group : det G be a compact, connected diegroup, LAMBDAG the space of free loops on G and p a prine. Then the following two conditions are equrialent :(1) The integral cohomology of G is p-toscn free(2) H^* (BLAMBDAG : */p)*H^* (BG : */p) <cross product> H^* (G : */p) as an algeha.a similon resutt for the Dwyer-Wilkerson H-space is also obtained.2. Infinite dimensional die groups : Topolegs of infinite dimesional die group (gauze groups)3. Morse homotopy type : det M be a conysact manifold and f : M*IR a Morse function. The homotopy type of M can be cletermined by f.Fukaya dofined a categary by f and described the quantum homotopy type of a syinplectic monifolds. I oftainea a method to describe the homotopy type of M by f, Morsover Ueno studiea confomal field theoy using algehaie geometory and Maruyama studied classifying spaces, moduli of verion connections and modubi of vectr bmdles.

科学研究助学金(C)05640105资助的研究成果包括以下几个方面。自由循环群：设G是一个紧的连通双群，LAMBDAG是G上自由循环的空间，p是素数。(2)H^*(BLAMBDAG：*/p)*H^*(BG：*/p)&lt；叉积&gt；H^*(G：*/p)作为代数，得到了Dwyer-Wilkerson H-空间的类似结果。无限维模组：无限维模组(纱线组)的极点3.Morse同伦型：det M是锥形流形，f：M*IR是Morse函数。F可以确定M的同伦型，Fukaya用f定义了范畴，刻画了辛流形的量子同伦型。用代数几何和Maruyama研究了分类空间、顶点连通模和向量模，得到了M的同伦型。

项目成果

河野明,入江幸右衛門: "Morse function and attaching map" J,Math,Kyoto,UniV. 35. 79-83 (1995)

Akira Kono，Koemon Irie：“莫尔斯函数和附加图”J，Math，Kyoto，UniV 35. 79-83（1995）。

上野健爾: "On confomal field theory" Proc,Durham Sym,on vector budles. (1995)

Kenji Ueno：“关于共角场论”Proc，Durham Sym，关于矢量包（1995）。

野村隆昭: "Grassmann manifold of JH algeha" Ann,Global Anal,Geom. 12. 237-260 (1994)

Takaaki Nomura：“JH algeha 的格拉斯曼流形”Ann，Global Anal，Geom。12. 237-260 (1994)

Takaaki Nomura: "Grassmann manifold of JH algeha" Ann.Global Anal.and Geon. Vol12. 237-260 (1994)

Takaaki Nomura：“JH algeha 的格拉斯曼流形”Ann.Global Anal.和 Geon。

Kenji Ueno: "On conformal field theory" Proc.Durham Sym.on vect bmdles. (to appear).

Kenji Ueno：“论共形场论”Proc.Durham Sym.on vect bmdles。