| Project/Area Number |
15340021
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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 | Graduate School of Science, Kyoto University |
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Principal Investigator |
KONO Akira Kyoto University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (00093237)
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| Co-Investigator(Kenkyū-buntansha) |
FUKAYA Kenji Kyoto University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (30165261)
NAKAJIMA Hiraku Kyoto University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (00201666)
KATO Kazuya Kyoto University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (90111450)
MORIWAKI Atsushi Kyoto University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (70191062)
HAMANAKA Hiroaki Hyogo University of Teacher Education, Department of Natural Science, Associate Professor, 学校教育学部, 助教授 (20294267)
神山 靖彦 琉球大学, 理学部, 助教授 (10244287)
國府 寛司 (国府 寛司) 京都大学, 大学院・理学研究科, 助教授 (50202057)
浅岡 正幸 京都大学, 大学院・理学研究科, 講師 (10314832)
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| Project Period (FY) |
2003 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥14,300,000 (Direct Cost: ¥14,300,000)
Fiscal Year 2005: ¥5,000,000 (Direct Cost: ¥5,000,000)
Fiscal Year 2004: ¥4,800,000 (Direct Cost: ¥4,800,000)
Fiscal Year 2003: ¥4,500,000 (Direct Cost: ¥4,500,000)
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| Keywords | self homotopy set / K-theory / classical group / gauge group / principal bundle / nilpotent group / exceptional group / characteristic class / モジュライ空間 / 自己ホモトピー群 / 例外リー群 / 分類空間 / 巾零群 / 局所化 / ホモトピー論 / ホモトピー代数 / nilpotency / LS category / 随伴束 / K-理論 / e-不変量 / KO理論 |
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| Research Abstract |
Akira Kono, the head investigator and Hiroaki Hamanaka, an investigator defined the unstable K-theory of a space X as the homotopy set [X, U(n)] and proved certain properties of it. Using the unstable K-theory they classified the homotopy types of gauge groups of principal SU(2)-bundles over the 6 dimensional sphere and SU(3)-bundles over the 4 dimensional sphere.
Akira Kono and Hideaki Oshima proved the self homotopy group [G, G] is not commutative for simple Lie group G of rank not less than 2. Hiroaki Hamanaka proved the nilpotent class of the self homotopy group of SU(n) is not less than 2 if n is greater than 4.
Akira Kono and Yasuhiko Kamiyama, an investigator determined the cohomology of the moduli space of SO(n)-instantons with instanton number 1.
Akira Kono proved a certain property of the Stiefel-Whitney classes of representations of exceptional Lie groups
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