Refinement of Gauge Theory and 4-dimensional topology
| Project/Area Number |
25400096
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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 | Osaka Medical College (2015-2017)
Gakushuin University (2013-2014) |
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Principal Investigator |
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| Research Collaborator |
ISHIDA Masashi 東北大学, 大学院理学研究科, 教授
MATSUO Shinichiroh 名古屋大学, 大学院多元数理科学研究科, 准教授
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | ゲージ理論 / トポロジー / 4次元多様体 / 山辺不変量 / 4次元トポロジー / 幾何学 / ４次元多様体 |
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| Outline of Final Research Achievements |
We have mainly investigated and developed the Pin(2)-monopole theory for applications to 4-dimensional topology and geometry. The results of this study are as follows: 1.Computations and applications of the Pin(2)-monopole invariants. In particular, the connected-sum formula, applications to exotic structures and computations of Yamabe invariants. 2.Formulation and computations of stable cohomotopy invariants. 3.Pin(2)-moopole theory on 4-manifolds with boundary and applications to intersection forms with local coefficients. 4.Nonvanishing theorem for almost Kaehler surfaces with real structures.
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Report
(6 results)
Research Products
(16 results)
