Dihedral semigroups, their defining relations and an application to describing knot semigroups of rational links

Vernitski Alexei; Tunsi Laila; Ponchel Colette; Lisitsa Alexei

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Dihedral semigroups, their defining relations and an application to describing knot semigroups of rational links

机译：Dihedral Semigroups，它们定义的关系和描述了解Rational Links结半群的应用程序

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摘要

It is known that a knot (link) is rational if and only if its -orbifold group is dihedral. A semigroup version of this result has been formulated as a conjecture. Working towards proving the conjecture, we describe certain semigroups associated with twist links, clarify how these semigroups are related to dihedral groups and find defining relations of these semigroups.

机译：众所周知，只有当其射线组是二面向的时，才有结（链接）是合理的。该结果的半群版本已被制定为猜想。努力努力证明猜想，我们描述了与扭曲链路相关的某些半群，阐明了这些半群与Dihedral组有关，并找到定义这些半群的关系。

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来源
《Semigroup Forum》 |2018年第1期|共12页
作者
Vernitski Alexei; Tunsi Laila; Ponchel Colette; Lisitsa Alexei;
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作者单位

Univ Essex Dept Math Sci Colchester Essex England;

Tripoli Univ Dept Math Tripoli Libya;

INSA Rouen St Etienne Du Rouvray France;

Univ Liverpool Dept Comp Sci Liverpool Merseyside England;

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原文格式 PDF
正文语种 eng
中图分类群的推广;
关键词
Cancellative semigroup; Knot semigroup; Rational knot; 4-plat; pi-orbifold group; Dihedral group;

机译：消除半群;结半群;理性结;4-PLET;PI-ORBIFOLD组;二面体组;

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1. Dihedral semigroups, their defining relations and an application to describing knot semigroups of rational links [J] . Vernitski Alexei, Tunsi Laila, Ponchel Colette, Semigroup Forum . 2018,第1期

机译：Dihedral Semigroups，它们定义的关系和描述了解Rational Links结半群的应用程序
2. EXPONENTIALLY　BOUNDED　C－SEMIGROUPS　AND　INTEGRATED　SEMIGROUPS　WITH　NONDENSELY　DEFINED　GENERATORS──Ⅲ：ANALYTICITY [J] . 郑权, 雷岩松数学物理学报：B辑英文版 . 1994,第001期

机译：带有非误定生成器的指数偏向的C-Semigrous和集成半群体──Ⅲ：分析性
3. EXPONENTIALLY BOUNDED C-SEMIGROUP AND INTEGRATED SEMIGROUP WITH NONDENSELY DEFINED GENERATORS I: APPROXIMATION: [J] . 郑权, 雷岩松数学物理学报：B辑英文版 . 1993,第003期

机译：指数界界的C-SEMIGROUP和集成半群，具有非密定定义的生成器I：近似：
4. Automated Reasoning for Knot Semigroups and 7r-orbifold Groups of Knots [C] . Alexei Lisitsa, Alexei Vernitski International conference onmathematical aspects of computer and information sciences . 2017

机译：结半群和7r-bifold群的自动推理
5. POWER COMMUTATIVE SEMIGROUPS AND THEIR CORRESPONDING RATIONAL LANGUAGES. [D] . DAVENPORT, DANIEL MARK. 1987

机译：功率交换半群及其对应的有理语言。
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7. Describing semigroups with defining relations of the form xy= yz and yx= zy and connections with knot theory [O] . Vernitski A 2017

机译：描述具有定义形式为xy = yz和yx = zy的关系的半群以及与结理论的联系

Dihedral semigroups, their defining relations and an application to describing knot semigroups of rational links

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