Topology of low dimensional manifolds with various geometric structures
| Project/Area Number |
20540072
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Kyoto University |
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Principal Investigator |
UE Masaaki Kyoto University, 大学院・理学研究科, 教授 (80134443)
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| Co-Investigator(Kenkyū-buntansha) |
FUJII Michihiko 京都大学, 大学院・理学研究科, 准教授 (60254231)
KATO Tsuyoshi 京都大学, 大学院・理学研究科, 教授 (20273427)
KATO Shinichi 京都大学, 大学院・理学研究科, 教授 (90114438)
USHIKI Shigehiro 京都大学, 大学院・人間・環境学研究科, 教授 (10093197)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 微分トポロジー / 3次元多様体 / 4次元多様体 / Seiberg-Witten理論 / 不変量 / ホモロジー3球面 / フレアホモロジー / 球面多様体 / 鉛管多様体 / 幾何学 / トポロジー / Floerホモロジー / Seiber-Witten理論 / 有理ホモロジー3球面 |
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| Research Abstract |
Masaaki Ue, the representative of this research has studied 3 and 4-manifolds, in particular 4-manifolds with boundary. We show that the two invariants for 3-manifolds, which are called Fukumoto-Furuta invariant and the correction term, coincide in case of spherical 3-manifolds. These invariants are derived from the two important theories for this area of research, Seiberg-Witten theory and Heegaard Floer homology theory. Moreover we show that these invariants are represented by the previously known eta invariants. We also give explicit constraints for the structures of 4-manifolds bounded by 3-manifolds of this type in terms of the Fukumoto-Furuta invariant.
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Report
(4 results)
Research Products
(21 results)
