2013 Fiscal Year Final Research Report
Study of invariants and geometric structures by local moves in Knot Theory
| Project/Area Number |
22540099
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Tokyo Woman's Christian University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
NIKKUNI Ryo 東京女子大学, 現代教養学部, 准教授 (00401878)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
NAKANISHI Yasutaka 神戸大学, 理学研究科, 教授 (70183514)
TANIYAMA Kouki 早稲田大学, 教育・総合科学学術院, 教授 (10247207)
|
|---|
| Research Collaborator |
HORIUCHI Sumiko 東京女子大学, 現代教養学部, 研究員 (40572144)
|
|---|
| Project Period (FY) |
2010-04-01 – 2014-03-31
|
| Keywords | 結び目 / 仮想結び目 / 局所変形 / 距離空間 / 有限型不変量 / C_n-move |
|---|
| Research Abstract |
A circle in the 3-dimensional space is called a knot. There exist many kinds of knot since the difference of the dimensions between a knot and a space where a knot exists is two. When we project a knot into the plane and give the over and under crossing information, we have the figure called a knot diagram. A knot whose any diagram has not only real crossings but also virtual crossings is called a virtual knot.
A local move is the operation which changes the local figure into another figure on a knot diagram. If two knots or two virtual knots can be transformed into each other by local moves, the minimal number of necessary local moves can be considered as a metric. We study relations between the positions of knots in the metric space of knots by a local move and knot invariants, and the property of this metric space, for example, the width of the metric space.
|
