| Project/Area Number |
13640224
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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 |
Global analysis
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| Research Institution | Waseda University |
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Principal Investigator |
KORI Tosiaki KORI,Tosiaki, 理工学部, 教授 (50063730)
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| Co-Investigator(Kenkyū-buntansha) |
鈴木 達夫 早稲田大学, 理工学部, 助手 (70318799)
本間 泰史 早稲田大学, 理工学部, 助手 (50329108)
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| Project Period (FY) |
2001 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 2003: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2002: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2001: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | Wess-Zumino-Witten actions / Axiomatic field theory / Conformally flat 4-manifolds / Dirac operator / Harmonic spinors / Residue theorem / Runge theorem / Riemann-Roch theorem / Conformally flat manifolds / WZWモデル / 調和スピノール / 共形平坦 / リーマン・ロッホ型定理 / 写像群の中心拡大 |
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| Research Abstract |
As for the project "Geometry of Field Theory" we gave a construction of the four-dimensional Wess-Zumino-Witten model. We proposed a definition of a Wess-Zumino-Witten action as a functor from the category conformally flat 4-manifolds to the category of line bundles with connection and gave a construction of it. This extends many phenomena discussed on 4-dimensional sphere to the class of conformally flat 4-manifolds with boundary, especially we succeeded to have Polyakov-Wiegner formula on such a manifold. We also obtained two dual types of abelian extension of the group of the smooth maps from 3-sphere to a Lie group. These results are published in Journal of Geometry and Physics, 47(2003).
As for the project "Spinor Analysis" we investigated various properties of harmonic spinors on conformally flat 4-manifolds, comprising (1)Integral representation (2)local existence of the solution, (3)Runnge's approximation theorem, Mittag-Lefler theorem, (4)global existence of solutions on domains of the Dirac equation. These results are published in the Japanese Journao of Mathematics, vol.28-1(2002), 1-30. Then investigations of this subject continue to ; (5)the introduction of meromorphic spinors on conformally flat manifolds and their devisors. (6)Riemann-Roch type theorem for the cohomology groups of meromorphic spinors. The results will be published in "Trends in Mathematics, Advances in Analysis and Geometry2, by Birkhauser publ..
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