| Project/Area Number |
25287009
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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 | Kyoto University |
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Principal Investigator |
Kato Tsuyoshi 京都大学, 理学(系)研究科(研究院), 教授 (20273427)
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| Co-Investigator(Kenkyū-buntansha) |
木田 良才 東京大学, 数理(科)学研究科(研究院), 准教授 (90451517)
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| Co-Investigator(Renkei-kenkyūsha) |
Kida Yoshikata 東京大学, 数理科学研究科, 准教授 (90451517)
Oguni Shin-ichi 愛媛大学, 理工学研究科, 准教授 (00549446)
Fukaya Tomohiro 首都大学, 東京理工学研究科, 准教授 (40583456)
Tsukamoto Masaki 京都大学, 理学研究科, 准教授 (70527879)
Matsuo Shinichiroh 名古屋大学, 多元数理科学研究科, 准教授 (40599487)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥15,600,000 (Direct Cost: ¥12,000,000、Indirect Cost: ¥3,600,000)
Fiscal Year 2016: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2015: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2014: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2013: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
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| Keywords | ゲージ理論 / 非可換幾何学 / モノポール写像 / 普遍被覆空間 / サイバーグウイッテン理論 / 無限次元ボット周期性 / 非コンパクト空間上の解析 / Lpコホモロジー / 離散群 / スペクトル解析 / モジュライ空間 / キャッソンハンドル / 非コンパクト多様体 |
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| Outline of Final Research Achievements |
I have constructed a monopole map over the universal covering space of a compact oriented smooth four manifold. We apply the infinite dimensional Bott periodicity by Higson-Kasparov-Trout. In particular its degree was given when the linearized map is isomorphic, as an element in the equivariant E theory. It produces a homomorphism between K group of C* algebras related to the group ring. It corresponds to a covering version of the Bauer-Furuta degree.
As an application, we proposed an aspherical 10/8 inequality for spin classifying 4 manifolds. We have also verified that it certainly holds for large class of 4 manifolds which includes complex minimal surfaces of general type.
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