| Project/Area Number |
09304005
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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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 | The University of Tokyo |
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Principal Investigator |
KOHNO Toshitake Graduate School of Mathematical Sciences, The University of Tokyo Professor, 大学院・数理科学研究科, 教授 (80144111)
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| Co-Investigator(Kenkyū-buntansha) |
MURAKAMI Jun Graduate School of Science, Osaka University, Associate Professor, 大学院・理学研究科, 助教授 (90157751)
SAITO Kyoji Research Institute for Mathematical Sciences, Kyoto University, Professor, 数理解析研究所, 教授 (20012445)
MORITA Shigeyuki Graduate School of Mathematical Sciences, The University of Tokyo, Professor, 大学院・数理科学研究科, 教授 (70011674)
SHIMIZU Yuji Graduate School of Science, Kyoto University, Lecturer, 大学院・理学研究科, 講師 (80187468)
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| Project Period (FY) |
1997 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥11,100,000 (Direct Cost: ¥11,100,000)
Fiscal Year 1999: ¥5,700,000 (Direct Cost: ¥5,700,000)
Fiscal Year 1998: ¥5,400,000 (Direct Cost: ¥5,400,000)
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| Keywords | conformal field theory / finite type invariants / loop space / configuration space / moduli space / Torelli group / 量子群 / 点の配置の空間 / チャーン・サイモンズ理論 / バシリエフ不変量 / カシャエフ予想 / ジョーンズ多項式 / 原始積分 / 組みひも群 / 写像類群 / ウィッテン不変量 / モノドロミー表現 / 位相的場の理論 / チャーン-サイモンズ摂動理論 / ファインマン図形 / 曲面のモジュライ空間 / グロモフ-ウィッテン不変量 |
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| Research Abstract |
We have made the following progress in conformal field theory, field theory, finite type topological invariants, moduli space of surfaces and the theory of period integrals. J. Murakami constructed a universal finite type invariant for 3-manifold in collaboration with T. Ohtsuki and others. Moreover, we discovered a relationship between such finite type invariants and the cohomology of the loop spaces of configuration spaces (T. Kohno). S. Morita investigated the geometry of the moduli space of compact Riemann surfaces as well as the structure of the mapping class group of surfaces mainly from the point of view of topology and established important results on the Torelli group. Y. Shimizu found an explecit description of the projectively flat connection for the conformal fieldtheory of Riemann surfaces of higher genera. The theory of elliptic root system due to K. Saito shead new lights on the study of primitive integrals in relation with topological field theory.
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