1999 Fiscal Year Final Research Report Summary
Classifying spaces of Categories, Flore Homology and Homotopsy Theory of Infinite Complexes
| Project/Area Number |
10440018
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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 Graduate School of Science, KYOTO UNIVERSITY, Professor, 大学院・理学研究科, 教授 (00093237)
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| Co-Investigator(Kenkyū-buntansha) |
KOKUBU Hiroshi Graduate School of Science, KYOTO UNIVERSITY, Associate Professor, 大学院・理学研究科, 助教授 (50202057)
FUKAYA Kenji Graduate School of Science, KYOTO UNIVERSITY, Professor, 大学院・理学研究科, 教授 (30165261)
MARUYAMA Masaki Graduate School of Science, KYOTO UNIVERSITY, Professor, 大学院・理学研究科, 教授 (50025459)
HAMANAKA Hiroaki Faculty on Teacher Education, Hyogo Univ.of Education, Lecturer, 学校教育学部, 講師 (20294267)
NAKAJIMA Hiraku Graduate School of Science, KYOTO UNIVERSITY, Associate Professor, 大学院・理学研究科, 助教授 (00201666)
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| Project Period (FY) |
1998 – 1999
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| Keywords | gauge group / free loop group / adjoint representation / Hopf space / Conley homology / Flore homology / Classifying space |
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| Research Abstract |
The most important results of the research project are the following :
(1) Topology of infinite dimensional Lie groups
(2) Morse theory of infinite dimensional manifolds
(3) Classifying space of categories and dynamical systems
For (1) we determined homology ring of free loop groups for 1-connected Lie groups completely. Using the result we are nou determining the cohomology of the classifying spaces of them. For gauge groups, we showed the case when the base spaces are closed 1-connectedmanifolds and the structure group is SU(2), the homotopy type of the classifying spaces completely determine the boinotopy type of the base space and the isomorphism class of the bundles.
For (2) K. Fukaya solved the Anord conjecture using the Gromov-Witten iavariants.
For (3) we considered the Conley homology. We considerd a certain category and the cohomology of the classifying space of it is isomorphic to the Conley homology under some fine coditions.
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