2002 Fiscal Year Final Research Report Summary
Algebraic Geometry, Differential Geometry and Topology of Manifolds
| 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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| Keywords | gauge group / infinite dimensional Lie group / localization / homotopyset / homotopy associative / Cherm number / homotopical algebra |
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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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