2005 Fiscal Year Final Research Report Summary
Homotopical Algebra and its Geometric Applications
| 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)
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| Project Period (FY) |
2003 – 2005
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| Keywords | self homotopy set / K-theory / classical group / gauge group / principal bundle / nilpotent group / exceptional group / characteristic class |
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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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