Gauge theory and localization
| Project/Area Number |
24340011
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Furuta Mikio 東京大学, 数理(科)学研究科(研究院), 教授 (50181459)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥11,180,000 (Direct Cost: ¥8,600,000、Indirect Cost: ¥2,580,000)
Fiscal Year 2015: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2014: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2013: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2012: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | トポロジー / 4次元多様体 / ゲージ理論 / 幾何学 / 微分トポロジー / 多様体上の解析 |
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| Outline of Final Research Achievements |
We investigated gauge theory on 4-manifolds using mathematical approach. While final outputs in physics are usually supposed to be some numbers, such as probabilities, it is known that we can construct some richer structures as outputs in the mathematical approach to gauge theory. Our goal is to find new properties of 4-manifolds using such rich structures. A major result of our research is a relation between the "signature" of a 4-manifold and the structure of the 3-manifold (Floer K gruop) which appears as its boundary.
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Report
(5 results)
Research Products
(22 results)
