1997 Fiscal Year Final Research Report Summary
Topology of manifolds and geometric structures
| Project/Area Number |
08454017
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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) |
KOKUBO Hiroshi Kyoto Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (50202057)
NISHIDA Goro Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (00027377)
MARUYAMA Masaki Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (50025459)
UENO Kenji Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (40011655)
FUKAYA Kenji Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (30165261)
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| Project Period (FY) |
1996 – 1997
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| Keywords | infinite dimensional Lie groups / free loop groups / gauge groups / moduli spaces / homoclinic orbits |
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| Research Abstract |
(1)Topology of infinite dimensional Lic groups
(2)Morse homotopy
Algebraic gcomctry and global analysis
Representation thcory and global analysis
(5)Dynamical systems
(1)A.Kono detcrmined the homotopy ring of free loop groups using the adjoint action of the groups on the based loop spaces. A.Kono also studied the problem of the relations between the isomorphic classcs of principal SU(2) bundles over a 1-counccted closcd 4-dimensional manifolds and the homotopy type of their classifying spaces and showed that the homotopy type of the classifying spaces almost detcrmined the isomorphic classcs of the bundles.
(2)K.Fukaya considered the family of Morsc functions on infinite dimensional spaces (e.g.moduli spaces)and defined sup products and cohomology operators using them.
(3)K.Ucno and Y.Shimizu considered problems on nonlincar differential cquations using algebraic geometry and obtained intercsting results on Kinizhink-Zamoldchikov cquations.
(4)M.Jimbo and T.Nomura obtained certain results on mathematical physics by using the methods of representation theory and quantum groups.
(5)H.lokubu studied various propertics on dynamical systems on manifolds and got results on homoclinic orbits.
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