2005 Fiscal Year Final Research Report Summary
Geometry and topology of 3-manifolds II
| Project/Area Number |
15204004
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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 | TOKYO INSTITUTE OF TECHNOLOGY |
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Principal Investigator |
KOJIMA Sadayoshi Tokyo Institute of Technology, Mathematical and Computing Sciences, Professor, 大学院・情報理工学研究科, 教授 (90117705)
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| Co-Investigator(Kenkyū-buntansha) |
YOSHIDA Tomoyoshi Tokyo Institute of Technology, Department of Mathematics, Professor, 大学院・理工学研究科, 教授 (60055324)
MORITA Shigeyuki University of Tokyo, Department of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (70011674)
MATSUMOTO Shigenori Nihon University, Department of Mathematics, Professor, 理工学部, 教授 (80060143)
SOMA Teruhiko Tokyo Denki University, Department of Mathematical Sciences, Professor, 理工学部, 教授 (50154688)
OHTSUKI Tomotada Kyoko University, Resaearch Institute of Mathematical Science, Associate professor, 数理解析研究所, 助教授 (50223871)
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| Project Period (FY) |
2003 – 2005
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| Keywords | hyperboloic geometry / cone manifold / 3-dimensional topology / secondary characteristic class / lamination / foliation / geometric structure / volume |
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| Research Abstract |
The purpose of this research project is to see the interaction of various geometric structures on 3-manifolds, to find principal idea behind them such as laws in physics and to promote the study of 3-manifolds interacting geometry and topology interdisciplinary. The current project based on the primary one that terminated on March 2003 was set up for 4 years and we have spent 3 years so far. Then we have decided to pre-renew the project by shifting the stress more on invariants because it seems to be necessary to do so in the light of recent progress on the current working subject. Fortunately, the new project was awarded as a continuing one and thus we here report our activity of the last 3 years.
In the last 3 years, we, the member of research group and collaborators, have promoted the project by doing research communication, organizing meetings and publishing research reports. As conclusion, we, the member of research group, have obtained a plenty of significant progress and simultaneously contributed the progress of this field. The research results were presented in the academic meetings including international ones. The details including one's by collaborators can be found in the attached report. In summary, according to the purpose of the project, we have darified what is needed for geometric methods to study topology of 3-manioflds more and more.
Looking at last 3 years, we must notice historical progress such as the solution of the ending lamination conjecture by Minsky-Brock-Canary the solution of Marden's conjecture by Agol and Calegari-Gabai and the approach to the geometrization by Hamilton and Perelman, which at least includes the solution of Poincare conjecture. Based on these, we set up the post geometrization by renewing our project with entitling "The geometry and invariants of 3-manifolds".
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