Study on quandle theory to classifying links up to link-homotopy

链路分类至链路同伦的Quandle理论研究

• 批准号: 23840014
• 负责人: INOUE Ayumu
• 金额: $ 2.08万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Research Activity Start-up
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-23840014/
• 关键词: トポロジー; 絡み目; カンドル; 絡み目ホモトピー

Link-homotopy gives rise to an equivalence relation on links which is weaker than ambient isotopy. A quandle is an algebraic system which is known to be useful to classifying links up to ambient isotopy. The aim of this study is to utilize quandles to classifying links up to link-homotopy. We introduced the notion of quasi-triviality of quandles, homology theory for quasi-trivial quandles, and obtained a lot of numerical link-homotopy invariants. We further explained the latent ability of those invariants.

链接同伦产生的等价关系的链接，这是弱于环境合痕。Quandle是一个代数系统，它被认为是有用的分类链接到环境合痕。本研究的目的是利用quandles分类链接同伦链接。我们引入了拟平凡性的概念和拟平凡性的同调理论，得到了大量的数值链同伦不变量。我们进一步解释了这些不变量的潜在能力。

项目成果

On the availability of quandle theory to classifying links up to link-homotopy

论 Quandle 理论对链接分类至链接同伦的可用性

• 发表时间: 2013
• 期刊: 京都大学数理解析研究所講究録「Intelligence of Low-dimensional Topology」(掲載決定)
• 作者: 土居啓司;吉田靖雄;長谷川幸雄;Ayumu Inoue
• 通讯作者: Ayumu Inoue

Toward obtaining a table of link-homotopy classes:The second homology group of a reduced knot quandle

获得链接同伦类表：简化结问题的第二同源群

• 发表时间: 2013
• 期刊: 京都大学数理解析研究所講究録「RIMS合宿型セミナーRepresentation spaces, twisted topological invariants and geometric structures of 3-manifolds」(掲載決定)
• 作者: 土居啓司;吉田靖雄;長谷川幸雄;Ayumu Inoue;Ayumu Inoue;Ayumu Inoue
• 通讯作者: Ayumu Inoue

QUASI-TRIVIALITY OF QUANDLES FOR LINK-HOMOTOPY

• DOI: 10.1142/s0218216513500260
• 发表时间: 2012-05
• 期刊: Journal of Knot Theory and Its Ramifications
• 影响因子: 0.5
• 作者: Ayumu Inoue

Quandle and link-homotopy

Quandle 和链接同伦

• 发表时间: 2012
• 作者: 土居啓司;吉田靖雄;長谷川幸雄;Ayumu Inoue;Ayumu Inoue;Ayumu Inoue;Ayumu Inoue;Ayumu Inoue;井上歩;Ayumu Inoue;Ayumu Inoue;Ayumu Inoue;井上歩;井上歩;Ayumu Inoue;井上歩;Ayumu Inoue
• 通讯作者: Ayumu Inoue

An approach to classifying links up to link-homotopy using quandle colorings

一种使用 quandle 着色将链接分类为链接同伦的方法

• 发表时间: 2012
• 作者: 土居啓司;吉田靖雄;長谷川幸雄;Ayumu Inoue;Ayumu Inoue;Ayumu Inoue;Ayumu Inoue;Ayumu Inoue;井上歩;Ayumu Inoue;Ayumu Inoue;Ayumu Inoue;井上歩;井上歩;Ayumu Inoue
• 通讯作者: Ayumu Inoue