Algebraic Geometry, Differential Geometry and Topology of Manifolds

代数几何、微分几何和流形拓扑

• 批准号: 12440017
• 负责人: KONO Akira
• 金额: $ 9.54万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-12440017/
• 关键词: gauge group; infinite dimensional Lie group; localization; homotopyset; homotopy associative; Cherm number; homotopical algebra; 無次元リー群; 分類空間; ホモトピー型; 随伴作用; スタック; 非可換代数幾何学

1. Homotopy theory of infinite dimensional Lie groups (gauge groups etc)A. Kono and S. Tsukuda partially solved the classification problem of the adjoint bundles of the principal bundles over finite complexes using the fibrewise homotopy theory. They determined the condition for the triviality of the adojoint bundle after the fibrewize localization. Note that gauge groups are the space of sections of the adojoint bundles.2. Unstable K-theoryA. Kono and H. Hamanaka determined the group of homotopy classes of maps from a 2n dimensional finite complex to U(n). On the other hand A. Kono and H. Oshima(Ibaraki Univ.) classified compact Lie groups whose self homotopy classes are commutative groups.3. Homotopical algebraHomotopical algebra is non -commutative homological algebra. A. Kono and A. Moriwaki considered application of homotopical algebra to alebraic geometry or arithmetic geometry. Applications to mathematical physics and string theory are considered by K. Fukaya.4. Dynamical systemAlgebraic invariants for 2-dimensional projective Anosov dynamical system are defined and several elementary properties of them are obtained by M. Asaoka(Kyoto Univ).

1.无限维李群(规范群等)的同伦理论：A.Kono和S.Tsukuda利用纤维同伦理论部分解决了有限复形上主丛的伴随丛的分类问题。在纤维化定位后，他们确定了伴随丛平凡的条件。请注意，规范群是共轭丛的截面的空间。不稳定K理论A。Kono和H.Hamanaka确定了从2n维有限复数到U(N)的映射的同伦类群。另一方面，A.Kono和H.Oshima(茨城大学)自同伦类为交换群的分类紧李群。同伦代数同伦代数是非交换的同调代数。河野和莫里瓦基考虑了同伦代数在代数几何或算术几何中的应用。K.Fukay.研究了数学物理和弦论的应用。定义了二维射影Anosov动力系统的代数不变量，并由M.Asaoka(京都大学)得到了它们的几个基本性质。

项目成果

A. Kono: "Topological characterrization of extensor product of BU"J. Math. Kyoto Univ.. to appear.

A. Kono：“BU 伸肌产物的拓扑表征”J。

A.Kono: "Commutativity of the group of self homotopy classes of Lie groups"Bull. London Math. Soc.. (掲載予定).

A.Kono：“李群的自同伦类群的交换性”，Bull，伦敦数学学会（待出版）。

Hiraku Nakajima : "Mckay correspondence and Hilbert schemes on dwrien them"Topology. 39. 1151-1191 (2000)

Hiraku Nakajima：“麦凯对应和希尔伯特方案对它们的描述”拓扑。

A.Kono: "On the cohomology of E8"J.Math.Kyoto Univ.. (掲載予定).

A.Kono：“论 E8 的上同调”J.Math.Kyoto Univ..（待出版）。

A.Kono: "On [X, U(n)] when dim X is 2n"J.Math.Kyoto Univ.. (掲載予定).

A.Kono：“当暗 X 为 2n 时，关于 [X，U(n)]”J.Math.Kyoto Univ..（待出版）。