The number of Cromwell moves needed for unknotting an arc-presentation of the trivial knot

解开小结的弧形表示所需的克伦威尔动作数量

• 批准号: 22540101
• 负责人: HAYASHI Chuichiro
• 金额: $ 2.33万
• 依托单位: Japan Women's 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 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540101/
• 关键词: 結び目理論; 自明結び目; アーク表示; クロムウェル変形; 位相幾何学; 幾何学

A knot is a circle in the 3-dimensional space R3. Every knot can be placed in a figure in the form of an open-book (a book opened so that every adjacent pair of pages are tangent to each other only in the biding) so that it intersects every page in a single arc). We call such a placement of a knot an arc-presentation. A knot is called trivial if it lies in a plane after being moved continuously. The trivial knot has an arc-presentation with two arcs. An example of infinite sequence of arc-presentations with n arcs of the trivial knot as below is given. They need linearly many exchange moves not changing the number of arcs with respect to n until they admit a merge move decreasing the number of arcs.

纽结是三维空间R3中的一个圆。每一个结都可以放在一个打开的书（一本书打开，使每一个相邻的页面是相切的，只有在biding）的形式，使它相交的每一页在一个单一的弧）的图形。我们把这种纽结的位置称为弧呈现。如果一个纽结在连续运动后位于一个平面内，则称之为平凡纽结。平凡纽结具有两条弧的弧表示。给出了平凡纽结的n条弧的无限弧表示序列的一个例子。他们需要线性许多交换移动不改变弧的数量相对于n，直到他们承认合并移动减少弧的数量。

项目成果

Unknotting number and number of Reidemeister moves neededfor unlinking

解链次数和解链所需的雷德迈斯特动作次数

• 发表时间: 2012
• 期刊: Topology and its Applications
• 影响因子: 0.6
• 作者: Chuichiro Hayashi;Miwa Hayashi andTahl Nowik
• 通讯作者: Miwa Hayashi andTahl Nowik

Genus two Heegaard splittings of1-genus 1-bridge knots II

1 属 1 桥结的属二 Heegaard 分裂 II

• 发表时间: 2012
• 期刊: SaitamaMathematical Journal
• 作者: Chuichiro Hayashi;Miwa Hayashi and Kanako Oshiro;Hiroshi Goda and Chuchiro Hayashi;Hiroshi Goda and Chuichiro Hayashi
• 通讯作者: Hiroshi Goda and Chuichiro Hayashi

Canonical forms for operation tables of finite connected quandles

有限连通二元运算表的规范形式

• 期刊: Communications in Algebra
• 影响因子: 0.7
• 作者: Chuichiro Hayashi;Miwa Hayashi;Tahl Nowik;Chuichiro Hayashi
• 通讯作者: Chuichiro Hayashi

Minimal unknotting sequence of Reidemeister moves containing unmatched RII moves

包含不匹配 RII 动作的 Reidemeister 动作的最小解结序列

• 发表时间: 2012
• 期刊: Journal of Knot Theory and its Ramifications
• 影响因子: 0.5
• 作者: Chuichiro Hayashi;Miwa Hayashi;Minori Sawada and Sayaka Yamada
• 通讯作者: Minori Sawada and Sayaka Yamada

Genus two Heegaard splittings of1-genus 1-bridge knots

1-属 1-桥结的属 2 Heegaard 分裂

• 发表时间: 2012
• 期刊: Kobe Journal of Mathematics
• 作者: Chuichiro Hayashi;Miwa Hayashi and Kanako Oshiro;Hiroshi Goda and Chuchiro Hayashi
• 通讯作者: Hiroshi Goda and Chuchiro Hayashi