| Project/Area Number |
12440017
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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 | Kyoto University |
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Principal Investigator |
KONO Akira Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (00093237)
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| Co-Investigator(Kenkyū-buntansha) |
KOKUBU Hiroshi Kyoto Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (50202057)
NAKAJIMA Hiraku Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (00201666)
FUKAYA Kenji Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (30165261)
HAMANAKA Hiroaki Hyogo Univ. of Education, Faculty on Teacher Education Lecturer, 学校教育学部, 講師 (20294267)
MOROWAKI Atsushi Kyoto Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (70191062)
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| Project Period (FY) |
2000 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥14,900,000 (Direct Cost: ¥14,900,000)
Fiscal Year 2002: ¥5,600,000 (Direct Cost: ¥5,600,000)
Fiscal Year 2001: ¥4,000,000 (Direct Cost: ¥4,000,000)
Fiscal Year 2000: ¥5,300,000 (Direct Cost: ¥5,300,000)
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| Keywords | gauge group / infinite dimensional Lie group / localization / homotopyset / homotopy associative / Cherm number / homotopical algebra / 無次元リー群 / 分類空間 / ホモトピー型 / 随伴作用 / スタック / 非可換代数幾何学 |
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| Research Abstract |
1. Homotopy theory of infinite dimensional Lie groups (gauge groups etc)
A. Kono and S. Tsukuda partially solved the classification problem of the adjoint bundles of the principal bundles over finite complexes using the fibrewise homotopy theory. They determined the condition for the triviality of the adojoint bundle after the fibrewize localization. Note that gauge groups are the space of sections of the adojoint bundles.
2. Unstable K-theory
A. Kono and H. Hamanaka determined the group of homotopy classes of maps from a 2n dimensional finite complex to U(n). On the other hand A. Kono and H. Oshima(Ibaraki Univ.) classified compact Lie groups whose self homotopy classes are commutative groups.
3. Homotopical algebra
Homotopical algebra is non -commutative homological algebra. A. Kono and A. Moriwaki considered application of homotopical algebra to alebraic geometry or arithmetic geometry. Applications to mathematical physics and string theory are considered by K. Fukaya.
4. Dynamical system
Algebraic invariants for 2-dimensional projective Anosov dynamical system are defined and several elementary properties of them are obtained by M. Asaoka(Kyoto Univ).
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