1995 Fiscal Year Final Research Report Summary
General study of topology
| Project/Area Number |
06302004
|
|---|
| Research Category |
Grant-in-Aid for Co-operative Research (A)
|
| Allocation Type | Single-year Grants |
|---|
| 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)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
KOJIMA Sadayoshi Tokyo Inst.of Technology fac.of sci.professor, 理学部, 教授 (90117705)
KAWAKUBO Katsuo Osaka Univ.fac.of sci.professor, 大学院・理学研究科, 教授 (50028198)
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 Period (FY) |
1994 – 1995
|
| Keywords | Knot theory / Homotopy theory / 4 dimensional manifold / Theory of singularity / Foliation / Mathematical physics / Transformation group / Dynamical system |
|---|
| 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 Seiberg-Witten theory and gave a new aspect in the theory of 4-dim 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.
|
