Spin^c Analysis for Group C^*-bundles on Manifolds and Study of Yamabe Invariants

流形上C^*-丛的自旋^c分析及Yamabe不变量的研究

• 批准号: 11640070
• 负责人: AKUTAGAWA Kazuo
• 金额: $ 2.18万
• 依托单位: Shizuoka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640070/
• 关键词: Yamabe Invariant; Conformal Geometry; Differential Topology; Symplectic Geometry; Spin^c Geometry; Descrete Group; Cobordism; Manifolds of Negative Curvature; シンプレクティック多様体; Seiberg-Witten理論; 群C^*環; ディラック作用素; K理論

We studied on Spin^c Analysis for Group C^*-bundles on Manifolds and Yamabe Invariants.More precisely, we studied on the fundamentals of C^*-algebras and their K-theory. We also studied on the synthetic research of Yamabe invariants and Bordism theory with supergroups (i.e., supergroups, supergroup-structures on manifolds, supergroup C^*-bunbles and others). In particular, by using this bordism theory with supergroups, we obtained an obstruction to the positivity of relative Yamabe invariants. This result is written in the following paper :Kazuo Akutagawa, An obstruction to the positivity of relative Yamabe invariants.The head investigator, Kazuo Akutagawa also studied with professor Boris Botvinnik (University of Oregon) on Yamabe invariants from the algebraic topological viewpoint. Similar to the Homology theory, we defined a natural relative version of the Yamabe invariant, that is, the "relative Yamabe invariant", and we studied on it and the relation of the Yamabe invariant of a double manifold. This result is also written in the following papers :Kazuo Akutagawa and Boris Botvinnik, Relative Yamabe invariant.Kazuo Akutagawa and Boris Botvinnik, Manifolds of positive scalar curvature and conformal cobordism theory.

我们研究了c^*组的自旋分析 - 在歧管上捆绑和yamabe不变。我们还研究了Yamabe不变性和Bordism理论的综合研究（即超组，超级组结构，超级组C^* - bumbles等）。特别是，通过将这种狂欢理论与超级组一起使用，我们获得了对相对山菜不变的积极性的阻碍。该结果写在以下论文中：kazuo akutagawa，妨碍了雅马布不变的相对积极性。首席调查员Kazuo Akutagawa还从Algebraic Topologicy topolication Pountolication the Yamabe Invariants上与Boris Botvinnik教授（University of Oregen of Oregon）一起学习。与同源性理论类似，我们定义了Yamabe不变的自然相对版本，即“相对的Yamabe不变”，我们研究了它及其Yamabe不变的关系的关系。该结果也写在以下论文中：Kazuo Akutagawa和Boris Botvinnik，相对的Yamabe不变。

项目成果

Hiroki Sato: "One-parameter families of extreme discrete groups for Jorgensen's inequality"Contemporary Math.(The First Ahlfors-Bers Colloquium). 256. 271-287 (2000)

Hiroki Sato：“Jorgensen 不等式的极端离散群的单参数族”当代数学。（第一届 Ahlfors-Bers 座谈会）。

Hiroki Sato: "One-parameter families of extreme discrete groups for J φrgensen's inequality"Contemporary Mathematics. (2000)

Hiroki Sato：“J φrgensen 不等式的极端离散群的单参数族”当代数学（2000 年）。

Reiko Aiyama and Kazuo Akutagawa: "Kenmotsu-Bryant type representation formulas for constant mean curvature surfaces in H^3(-c^2) and S^3_1(c^2)"Annals of Global Analysis and Geometry. 17. 49-75 (1999)

Reiko Aiyama 和 Kazuo Akutakawa：“H^3(-c^2) 和 S^3_1(c^2) 中恒定平均曲率曲面的 Kenmotsu-Bryant 型表示公式”全局分析与几何年鉴。

Hironori Kumura: "A note on the absence of eigenvalues on negatively curved manifolds"Kyusyu J.Math.. (印刷中).

Hironori Kumura：“关于负弯曲流形上不存在特征值的注释”Kyusyu J.Math..（出版中）。

Yoshihide Okumura: "Lifting problem and its application to Riemann surfaces"The Eighth International Conference on Complex Analysis. (to appear).

Yoshihide Okumura：“提升问题及其在黎曼曲面上的应用”第八届国际复分析会议。