2014 Fiscal Year Final Research Report
Theory of local index and geometric quantization
| Project/Area Number |
24540095
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Meiji University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2012-04-01 – 2015-03-31
|
| Keywords | 解析的指数 / Witten摂動 / 局所化 / 幾何学的量子化 |
|---|
| Outline of Final Research Achievements |
For the previous joint work with M. Furuta and H. Fujita on an index theory for Dirac type operators on possibly non-compact Riemannian manifolds based on the idea of Witten's deformation, I investigated the dependence of the index on additional geometric structures which are used to define the index from the viewpoint of the cobordism. I also investigated the formulation of our theory by using the K-theory. Furthermore I investigated the relationship between other researches and ours, and applied our index theory to geometric quantization and other research area.
|
| Free Research Field |
シンプレクティック幾何学
|
