2015 Fiscal Year Final Research Report
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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| Keywords | トポロジー / 4次元多様体 / ゲージ理論 |
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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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| Free Research Field |
幾何学
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