Non-Commutative Geometry and the Spectral Flow Index Theorem

非交换几何和谱流指数定理

基本信息

批准号：
12640086
负责人：
MORIYOSHI Hitoshi
金额：
$ 2.18万
依托单位：
Keio University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640086/
关键词：
NONCOMMUTATIVE GEOMETRY K-TEHORY THE INDEX THEOREM SPECTRAL FLOW CYCLIC COHOMOLORY K-THEORY

项目摘要

In this research we proceeded to a generalization of the Atiyah-Singer index theorem on the bas1S of Low dimensional Topology. The objective of the project are the followings:1. Establish the elaborated Index Theorem in the framework of Non-commutative Geometry. Also study the relationship between the Index Theorem and the analytic secondary invariants like the eta invariants and the spectral flow;2. Study the relationship between the elaborated Index Theorem and secondary characteristic classes including the Maslov class.Here we state one of the results of the project, which is related to the Atiyah-Patodi-Singe Index Theorem in Non-commutative Geometry. In July 2001, we are invited to give a talk with the title 'Analytic K-theory and the index theorem' at Topology Symposium of Japan, Akita. We are also working on the project are presented with the title 'Eta invariants, the Godbillon-Vey classes and the index theorem' in March 2001 at Workshop on Non-commutative Geometry and String Theory, Keio University. We also developed the research on Non-commutative Hopf invariants, and presented some results at Nagoya Technology Institute with the title 'Spectral flow, the Teoplitz index and the Hopf invariant' in March 2001, and with the title 'A index theorem of vector field and the Hopf invariant' at Kagoshima University in February 2002.

在这项研究中，我们对低维拓扑的BAS1进行了Atiyah-Singer索引定理的概括。该项目的目的是以下内容：1。在非共同几何形状的框架中建立详细的索引定理。还要研究索引定理与分析次级不变式之间的关系，例如ETA不变性和光谱流； 2。研究详细指数定理与包括Maslov类在内的二级特征类别之间的关系。在这里，我们陈述了该项目的结果之一，这与非交通性几何形状中的Atiyah-Patodi-Singe指数相关。 2001年7月，我们被邀请与日本拓扑座谈会的标题“分析K理论和索引定理”进行演讲。我们还在研究该项目的工作中介绍了标题“ ETA不变性，Godbillon-Weave类和指数定理”，2001年3月在Keio University的非交通性几何学和弦乐理论研讨会上。我们还开发了有关非交通型HOPF不变性的研究，并在2001年3月的标题“光谱流，Teoplitz Index和Hopf Invariant”的标题“频谱流，Teoplitz Index和Hopf Invariant”上呈现了一些结果，并在2002年费用的Kagoshima University的标题为“ Vector Field and Hopf Invariant”的标题为“索引定理”。