Characterization of the quantum and the finite type link invariants via the algebraic links.

通过代数链接表征量子和有限类型链接不变量。

• 批准号: 16540091
• 负责人: NAKABO Shigekazu
• 金额: $ 1.02万
• 依托单位: Kurume National College of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540091/
• 关键词: finite type invariant; quantum invariant; algebraic link; 2-bridge link; Kauffman polynomial; Q-polynomial; Chebyshev ppolynomial

There are several approaches to describe the relationships between the finite type invariants and the quantum invariants of knots and links. The main purpose of this research is to characterize the finite type link invariants by the quantum link invariants via the algebraic links.The author had given explicit formulas of HOMFLY and Jones polynomials for 2-bridge links, which is a family of specific links belonging to the algebraic links. We proceeded to investigate the other quantum invariants for 2-bridge links.As a result, we had a formula to describe the Q and Kauffman polynomials for 2-bridge links in terms of Chebyshev polynomials, through the computational experiments based on the method given by Lickorish which presents the Q and Kauffman polynomials by matrix manipulations.It is well-known that he Chebyshev polynomial is deeply related to various areas in mathematical science or engineering, especially the number theory, combinatrics, approximation theory etc. We expect our formulas to connect the different objects or areas to the knot theory.

有几种方法可以描述有限型不变性与结和链接的量子不变性之间的关系。这项研究的主要目的是通过代数链接表征量子链接不变的有限型链接不变。代数链接。我们开始研究2桥链接的其他量子不变性。结果，我们有一个公式来描述Q和Kauffman的多项式，以Chebyshev的多项式来描述2桥链接，该公式通过基于计算实验的方法，基于计算实验。 lickorish通过矩阵操作呈现Q和the Q.Auffman的多项式。结理论的不同对象或区域。

项目成果

2橋絡み目のQ多項式のチェビシェフ多項式による表示

两桥Q多项式用切比雪夫多项式表达

• 发表时间: 2007
• 期刊: 久留米工業高等専門学校紀要 22・2
• 作者: M.Gameiro;T.Gedeon;W.Kalies;H.Kokubu;K.Mischaikow;H.Oka;中坊滋一
• 通讯作者: 中坊滋一

Q-Polynomial of 2-bridge links in terms of Chebyshev polynomials

用切比雪夫多项式表示的 2 桥链路的 Q 多项式

• 发表时间: 2007
• 期刊: Memoirs of Kurume National College of Technology 22-2
• 作者: T.Ito;B.Scardua;Shigekazu Nakabo
• 通讯作者: Shigekazu Nakabo