1997 Fiscal Year Final Research Report Summary
COMPREHENSIVE STUDY OF TOPOLOGY
| Project/Area Number |
08304006
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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 | University of Tokyo |
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Principal Investigator |
MORITA Shigeyuki University of Tokyo Professor, 大学院・数理科学研究科, 教授 (70011674)
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| Co-Investigator(Kenkyū-buntansha) |
KOJIMA Sadayosi Tokyo Inst.Tech.Professor, 大学院・情報理学工学研究科, 教授 (90117705)
KAWAUCHI Akio Osaka City Univ.Professor, 理学部, 教授 (00112524)
MATUMOTO Takao Hiroshima Univ.Professor, 理学部, 教授 (50025467)
KAWAKUBO Katsuo Osaka University Professor, 大学院理学研究科, 教授 (50028198)
NISHIDA Goro Kyoto University Professor, 大学院・理学研究科, 教授 (00027377)
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| Project Period (FY) |
1996 – 1997
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| Keywords | 3 manifolds / homotopy theory / transformation theory / gauge theory / singularity theory / dynamical systems / foliation / moduli space |
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| Research Abstract |
We have organized number of workshops on various important topics in topology and in each of them we made lectures and discussions. More concretely, our principal results are as follows.
(i) We have made a great development in topology and geometry of 3 and 4 dimensional manifolds. In particular, we obtained a worldwide result concerning topological invariants of 3 manifolds. We also have great success in the study of hyperbolic geometry and knot theory.
(ii) As to homotopy theory and transformation thoery, we went over former points of view to obtain new results which have close connection with algebraic K-theory, number theory as well as algebraic geometry.
(iii) We obtained essentially new results concerning the topology of the moduli space of Riemann surfaces.
(iv) We added new developments in singularity theory, dynamical systems and the theory of foliations.
(v) We have achieved deeper understanding of the symplectic geomtry in connection with the gauge theory and mathematical physics.
(vi) We have begun a new project to persue theoretical interface between topology and computer science.
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Research Products
(14 results)
