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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

基本信息

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

项目摘要

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.

我们研究了流形和Yamabe不变量上群C^*-丛的自旋^c分析，更确切地说，我们研究了C^*-代数的基本原理及其K-理论。我们还研究了Yamabe不变量和Bordism理论与超群(即超群、流形上的超群结构、超群C^*-群等)的综合研究。特别地，利用超群的边界理论，我们得到了相对Yamabe不变量正性的一个障碍。这一结果写在下列文章中：Akutagawa Kazuo Akutagawa，阻碍相对Yamabe不变量的正性。首席研究员Kazuo Akutagawa还与俄勒冈大学的Boris Botvinnik教授从代数拓扑的观点研究了Yamabe不变量。类似于同调理论，我们定义了Yamabe不变量的一个自然相对形式，即“相对Yamabe不变量”，并研究了它与二重流形的Yamabe不变量之间的关系。这一结果也被写在下列论文中：Akutagawa Kazuo和Boris Botvinnik，相对Yamabe不变量，Kazuo Akutagawa和Boris Botvinnik，正标量曲率流形和共形余边理论。