Construction and Classification of Weaves

组织结构和分类

• 批准号: 22J13397
• 负责人: MAHMOUDI Sonia
• 金额: $ 1.09万
• 依托单位: Tohoku University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for JSPS Fellows
• 财政年份: 2022
• 资助国家: 日本
• 起止时间: 2022-04-22 至 2024-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22J13397/
• 关键词: knot theory; low-dimensional topology; weave; link thickened torus; periodic tilings; topological invariants; entanglement

The purpose of this research was to define, construct, and classify periodic weaves as new topological objects. To construct weaves, our approach has been improved using combinatorial arguments and we developed new weaving invariants to classify them using knot theory. In particular, we developed the 'polygonal link methods' which allow one to build and classify weaves using tiling theory. More specifically, given a doubly periodic tiling of the plane and a polygonal link method, by instructing how to cover edges and vertices of the tiling by strands, we introduced a systematic algorithm to predict, distinguish, construct and classify weaving motifs and other entangled structures such as polycatenane and mixed motifs. Then, we started a classification of weaves by their symmetry groups.

这项研究的目的是将周期性编织定义为新的拓扑对象。为了构建编织，我们使用组合论点改善了我们的方法，我们开发了新的编织不变性，以使用结理论对它们进行分类。特别是，我们开发了“多边形链接方法”，该方法允许人们使用瓷砖理论构建和分类编织。更具体地说，如果平面的双重周期性平铺和多边形链接方法，通过指导如何覆盖链的边缘和顶点，我们引入了一种系统的算法，以预测，区分，构建和分类编织基序和其他纠缠结构，例如多结构和混合基序。然后，我们开始了他们的对称组对编织的分类。

项目成果

NTUA Athens(ギリシャ)

NTUA 雅典（希腊）

Periodic Weaving Diagrams

周期性编织图

• 发表时间: 2022
• 作者: Mizuki Fukuda;Motoko Kotani;and Sonia Mahmoudi;Sonia Mahmoudi;Sonia Mahmoudi;Sonia Mahmoudi;Sonia Mahmoudi;Sonia Mahmoudi
• 通讯作者: Sonia Mahmoudi

The 18th Mathematics Conference for Young Researchers : MCYR18

第十八届青年研究人员数学会议：MCYR18

• DOI: 10.14943/101654
• 发表时间: 2022
• 期刊: Hokkaido University technical report series in Mathematics
• 作者: Ishibashi Kazuki;Ishibashi Kazuki;Ishibashi Kazuki;Jitsuro Sugie and Kazuki Ishibashi;Ishibashi Kazuki;Ishibashi Kazuki
• 通讯作者: Ishibashi Kazuki

Doubly Periodic Weaves & Polycatenanes

双周期组织

• 发表时间: 2022
• 作者: Mizuki Fukuda;Motoko Kotani;and Sonia Mahmoudi;Sonia Mahmoudi
• 通讯作者: Sonia Mahmoudi

University of Potsdam(ドイツ)

波茨坦大学（德国）