Study of invariants and geometric structures by local moves in Knot Theory

通过结理论中的局部移动研究不变量和几何结构

• 批准号: 22540099
• 负责人: OHYAMA Yoshiyuki
• 金额: $ 2.75万
• 依托单位: Tokyo Woman's Christian University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540099/
• 关键词: 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; Vassiliev不変量; C_n-distance

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.

三维空间中的一个圆称为一个结。由于纽结与其所在空间的维数之差为2，所以纽结的种类很多。当我们将一个纽结投影到平面上并给出上下交叉信息时，我们就得到了一个称为纽结图的图形。任何图既有真实的交叉又有虚拟交叉的纽结称为虚拟纽结。局部移动是将纽结图上的局部图形改变为另一图形的操作。如果两个节点或两个虚拟节点可以通过局部移动相互转换，则所需局部移动的最小数量可以被认为是度量。研究了纽结在度量空间中的位置与纽结不变量的关系，以及度量空间的性质，如度量空间的宽度.

项目成果

A two dimensional lattice of knots by C_<2n>-moves

由 C_<2n> 移动的二维结点阵

• 发表时间: 2010
• 作者: 堀内澄子;大山淑之
• 通讯作者: 大山淑之

A numerical invariant for two component spatial graphs

二分量空间图的数值不变量

• 发表时间: 2010
• 期刊: Journal of Knot Theory and its Ramificationsに掲載決定 未定
• 作者: Sumiko Horiuchi;Yoshiyuki Ohyama;Sumiko Horiuchi
• 通讯作者: Sumiko Horiuchi

A two dimensional lattice of knots by C_n–moves

由 C_n 移动的二维结点阵

• 发表时间: 2012
• 作者: 堀内澄子;大山淑之
• 通讯作者: 大山淑之

A two dimensional lattice of knots by C_n-moves

C_n-moves 的二维结点阵

• 发表时间: 2012
• 作者: 堀内澄子;大山淑之;Naotsugu Chinen and Tetsuya Hosaka;大山淑之
• 通讯作者: 大山淑之

Yoshiyuki Ohyama's home page

大山由之的主页