Project/Area Number  10440017 
Research Category 
GrantinAid for Scientific Research (B).

Section  一般 
Research Field 
Geometry

Research Institution  Tokyo Institute of Technology 
Principal Investigator 
KOJIMA Sadayoshi Tokyo Institute of Technology, Material and Computing Sciences, Professor, 情報理工学研究科, 教授 (90117705)

CoInvestigator(Kenkyūbuntansha) 
OHTSUKI Tomotada Tokyo Institute of Technology, Department of Mathematical and Computing Sciences, Associate Professor, 情報理工学研究科, 助教授 (50223871)
YAMAGUCHI Takao Kyushu University, Department of Mathematics, Professor, 大学院・数理学研究科, 教授 (00182444)
SOMA Teruhiko Tokyo Denki University, Department of Mathematical Sciences, Professor, 理工学部, 教授 (50154688)
MORITA Shigeyuki University of Tokyo, Department of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (70011674)
YOSHIDA Tomoyoshi Tokyo Institute of Technology, Department of Mathematics, Professor, 大学院・理工学研究科, 教授 (60055324)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥8,800,000 (Direct Cost : ¥8,800,000)
Fiscal Year 1999 : ¥3,500,000 (Direct Cost : ¥3,500,000)
Fiscal Year 1998 : ¥5,300,000 (Direct Cost : ¥5,300,000)

Keywords  hyperbolic geometry / conemanifold / 3manifold / deformation / geometric structure / rigidity / Dehn filling / knot / 双曲幾何学 / 錐多様体 / 3次元多様体 / 変形 / 幾何構造 / 剛体性 / Dehn手術 / 結び目 / 3次元トポロジー 
Research Abstract 
The aim of this project was to develop the deformation theory of conemanifolds from interdisciplinary viewpoints and to apply it to the theory of topology of 3manifolds, base on our previous related works. The starting point was the workshop "Conemanifolds and hyperbolic geometry" which we held on July '98 at Tokyo Institute of Technology. Summarizing related works up to those days, we reconfirmed an attraction and power of the deformation method of cone structures. Then reflecting on much attention for geometric understanding of Dehn fillings in the workshop, we have developed the theory of deformation of cone structures and topology of 3manifolds, emphasizing the connection with gauge theory, mapping classes, collapsings, Kleinian groups and quantum invariants, by having many discussions and small intensive meetings for two years. We also printed a few informal booklets which collected several research drafts, and distributed them to the institutions and researchers for their convenience. The concluding symposium "geometric topology of 3manifolds" on January '00 summarized the results on 3manifolds by geometric method in the last two years and discussed the prospect of the research. There are many interactions between several aspects of 3manifolds recently and the study of 3manifolds by geometric method seems to get into new stage. In view of these circumstance, our project clarified that geometric method in finding mathematical structures behind appearance became important for the future in which presentations of characteristics would interact more.
