2010 Fiscal Year Final Research Report
gauge theory and homotopy theory
| Project/Area Number |
19340015
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | The University of Tokyo |
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Principal Investigator |
FURUTA Mikio 東京大学, 大学院・数理科学研究科, 教授 (50181459)
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| Co-Investigator(Kenkyū-buntansha) |
KATO Tsuyoshi 京都大学, 理学研究科, 教授 (20273427)
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| Co-Investigator(Renkei-kenkyūsha) |
TSUBOI Shun 東京大学, 大学院・数理科学研究科, 教授 (40114566)
UE Masaaki 京都大学, 理学研究科, 教授 (80134443)
MINAMI Norihiko 名古屋工業大学, 工学研究科, 教授 (80166090)
KAMETANI Yukio 慶應義塾大学, 理工学部, 准教授 (70253581)
HAYASHI Shuhei 東京大学, 大学院・数理科学研究科, 准教授 (20247208)
KAWAZUMI Nariya 東京大学, 大学院・数理科学研究科, 准教授 (30214646)
TAMAKI Dai 信州大学, 理学部, 教授 (10252058)
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| Research Collaborator |
KIYONO Kazuhiko 東京大学, 大学院・数理科学研究科, 助教 (40234398)
YOSHIDA Takahiko 明治大学, 研究員 (70451903)
FUJITA Hajime 学習院大学, 理学部, 助教 (50512159)
NAKAMURA Nobuhiro 東京大学, 大学院・数理科学研究科, 特任助教 (10512171)
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| Project Period (FY) |
2007 – 2010
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| Keywords | トポロジー / 位相幾何 / 幾何学 |
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| Research Abstract |
We investigated shape of 4-dimensional spaces using partial differential equations which were related to physics.
(1) Formulation of a Pontrjagin-Thom construction to describe the stable homotopy version of the Seiberg-Witten invariant(joint with Tian-Jun Li).
(2) Construction of a local coefficient version of the Seiberg-Witten monopole equation. As an application Nobuhiro Nakamura obtained a restriction on the intersection form of 4-dimensional smooth manifolds with local coefficients.
(3) Clarification and generalization for the mechanism of the localization of the index of Dirac operators on symplectic manifolds to Bohr-Sommerfeld orbits(joint with Takahiko Yoshida and Hajime Fujita.)
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