| Project/Area Number |
09304011
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (A)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Osaka City University |
|---|
Principal Investigator |
KAWAUCHI Akio Osaka City Univ., Dept. of Math., Prof., 理学部, 教授 (00112524)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
KANENOBU Taizo Osaka City Univ., Dept. of Math., Associate Prof., 理学部, 助教授 (00152819)
SAKUMA Makoto Osaka Univ., Inst. Of Math., Associate Prof., 理学研究科, 助教授 (30178602)
NAKANISHI Yasutaka Kobe Univ., Dept. of Math., Prof., 理学部, 教授 (70183514)
MATUMOTO Takao Hiroshima Univ., Dept. of Math., Prof., 理学部, 教授 (50025467)
MATSUMOTO Yukio Tokyo Univ., Inst. Of Math., Prof., 数理科学研究科, 教授 (20011637)
|
|---|
| Project Period (FY) |
1997 – 1999
|
| Project Status |
Completed (Fiscal Year 1999)
|
| Budget Amount *help |
¥27,100,000 (Direct Cost: ¥27,100,000)
Fiscal Year 1999: ¥10,700,000 (Direct Cost: ¥10,700,000)
Fiscal Year 1998: ¥10,200,000 (Direct Cost: ¥10,200,000)
Fiscal Year 1997: ¥6,200,000 (Direct Cost: ¥6,200,000)
|
|---|
| Keywords | Knot theory / manifold / topology / exact 4-manifold / Arf invariant / hyperbolic geometry / molecular graph / DNA knot / 多様体論 / 力学系 / 特異点論 / 変換群論 / 位相数学 / ホモトピー論 / 特異点 / 接触幾何 / シンプレクティック幾何 / グラフ理論 / 変換群 / 結び目 / イミテーション理論 / 絡み目の2次形式 / Vassilier不変量 / リボン結び目 / 結び目解消数 / フォード基本領域 / 穴開きトーラス |
|---|
| Research Abstract |
It is well-known that in order to study a geometry of manifold, it is important to study the topological structure. The study of topology is to analyze the position and the shape of a topological object, and the study of position is to analyze a pair of manifold and submanifold, represented typically by knot theory. Knot theory and related topics are studied actively for the last two decades not only abroad but also much more in Japan. During this research program, knot theory and the related studies of low dimensional manifolds have been studied by many researchers. For example, Kawauchi obtained a new concept "exact 4-manifold" by studying a surface-knot. This concept is useful to classify 4-manifolds with infinite cyclic first homology, and as a result, we see that there exists a surface-knot invariant which is analogous to the Arf invariant of a classical knot. In other related studies, hyperbolic geometry, differential topology (including handle theory, Morse theory), gauge theory, transformation theory, foliation theory, homotopy theory, real and complex singularities, dynamical systems, general topology, surface moduli have been studied. Also, a "mew applied knot theory" was searched in relations with Yang-Baxter equation (in statistical mechanics), a molecular graph (in molecular chemistry), and DNA knot (in biochemistry).
|
