Theory of local index and geometric quantization
| Project/Area Number |
24540095
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Meiji University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 解析的指数 / Witten摂動 / 局所化 / 幾何学的量子化 / Dirac作用素 / Witten 摂動 |
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| 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.
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Report
(4 results)
Research Products
(13 results)
