1999 Fiscal Year Final Research Report Summary
Topological Field Theory and Related Geometry
| 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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| Keywords | conformal field theory / finite type invariants / loop space / configuration space / moduli space / Torelli group |
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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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