| Project/Area Number |
25400085
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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 | Nagoya University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
NATSUME TOSHIKAZU 名古屋工業大学, 工学系研究科, 教授 (00125890)
MAEDA YOSHIAKI 慶應義塾大学, 理工学部, 教授 (40101076)
MITSUMATSU YOSHIHIKO 中央大学, 理工学部, 教授 (70190725)
ONO KAORU 京都大学, 数理解析研究所, 教授 (20204232)
MIYAZAKI NAOYA 慶應義塾大学, 経済学部, 教授 (50315826)
TAKAKURA TATSURU 中央大学, 理工学部, 教授 (30268974)
TATE TETSUYA 名古屋大学, 大学院多元数理科学研究科, 准教授 (00317299)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 指数定理 / 非可換幾何 / 葉層多様体 / Godbillon-Vey 不変量 / K理論 / 巡回コホモロジー / Godbillon-Vey不変量 |
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| Outline of Final Research Achievements |
First, we extended the index theorem to fractal sets such as the Cantor set and the Sierpinski gasket. Second, by exploiting the framework of Noncommutative Geometry we generalized the Atiyah-Patodi-Singer index theorem to a Galois covering of compact manifold with boundary, which gives a formula for the pairing between K-group and cyclic cohomology. Third, we clarified the relation of the Dixmier-Douady class and the Godbillon-Vey class, which respectively appears as a characteristic class for Gerbe and foliated circle bundles. It turned out that they are connected via the Cheeger-Chern-Simons invariant. As a byproduct we succeeded to describe the universal central extension of circle diffeomorphism group in terms of the Calabi invariant.
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