Project/Area Number  06302004 
Research Category 
GrantinAid for Cooperative Research (A).

Research Field 
Geometry

Research Institution  KYOTO UNIVERSITY 
Principal Investigator 
NISHIDA Goro Kyoto Univ.fac.of sci.professor, 大学院・理学研究科, 教授 (00027377)

CoInvestigator(Kenkyūbuntansha) 
佐藤 肇 名古屋大学, 理学部, 教授 (30011612)
松元 重則 日本大学, 理学部, 教授 (80060143)
松本 幸夫 東京大学大学院, 数理科学研究所, 教授 (20011637)
森田 茂之 東京工業大学, 理学部, 教授 (70011674)
KAWAKUBO Katsuo Osaka Univ.fac.of sci.professor, 大学院・理学研究科, 教授 (50028198)
KOJIMA Sadayoshi Tokyo Inst.of Technology fac.of sci.professor, 理学部, 教授 (90117705)
KAWAUCHI Akio Osaka City Univ.fac.of sci.professor, 理学部, 教授 (00112524)
KATO Hisao Tsukuba Univ.Math.Professor, 数学系, 教授 (70152733)
OKA Mutsuo Tokyo Metropolitan Univ.sci.Professor, 理学部, 教授 (40011697)

Project Fiscal Year 
1994 – 1995

Project Status 
Completed(Fiscal Year 1995)

Budget Amount *help 
¥20,000,000 (Direct Cost : ¥20,000,000)
Fiscal Year 1995 : ¥9,300,000 (Direct Cost : ¥9,300,000)
Fiscal Year 1994 : ¥10,700,000 (Direct Cost : ¥10,700,000)

Keywords  Knot theory / Homotopy theory / 4 dimensional manifold / Theory of singularity / Foliation / Mathematical physics / Transformation group / Dynamical system / 結び目理論 / ホモトピー論 / 4次元多様体 / 特異点論 / 葉層構造理論 / 数理物理学 / 変換群 / 力学系 / 接触幾何学 / トポロジー / 特異点 / 葉層構造 / 結び目 / 多様体 
Research Abstract 
The first big achievement in the study of topology was the classification theory of manifolds by Thom, Milnor, Smale et al in 1960's. These researches were more or less properly topological ones in their subjects or methods, but in 70's various attempts to relate those results to other fields of mathematics were made and the Donaldson theory in 4 dim manifolds proved such attempts would be successful. In our research program, most of research groups in topology studied actively not being in the traditional fields. Yukio Matsumoto and his group studied the SeibergWitten theory and gave a new aspect in the theory of 4dim manifolds. Groups of dynamical system, theory of singularities and foliation theory made not only traditional researches but also made cooperative study on some themes like topological study of algebraic variety or symplectic geometry, and in the theory of transformation groups good results on the action of algebraic groups were obtained. In the homotopy theory studies of new direction, for example, study of relations between elliptic cohomology and number theory or homotopical study of certain moduli spaces have been done. Kenji Fukaya and his group are working in a field overlapping most fields mentioned above, and have obtained remarkable results about the topological field theory, Arnold conjecture and Novikov conjecture. The group of knot theory, one of the most active group in topology, obtained numbers of results using a new method of mathematical physics as well as traditional methods. They will publish their results at the international conference on knot theory in Tokyo held in July 1996.
