通过对两个结的二重进行管道运算得到的结的3环多项式

IF 0.6 4区数学 Q3 MATHEMATICS

International Journal of Mathematics Pub Date : 2023-09-01 DOI:10.1142/s0129167x23500866

Kouki Yamaguchi

{"title":"通过对两个结的二重进行管道运算得到的结的3环多项式","authors":"Kouki Yamaguchi","doi":"10.1142/s0129167x23500866","DOIUrl":null,"url":null,"abstract":"The 3-loop polynomial of a knot is a polynomial presenting the 3-loop part of the Kontsevich invariant of knots. In this paper, we calculate the 3-loop polynomial of knots obtained by plumbing the doubles of two knots; this class of knots includes untwisted Whitehead doubles. We construct the 3-loop polynomial by calculating the rational version of the Aarhus integral of a surgery presentation. As a consequence, we obtain an explicit presentation of the 3-loop polynomial for the knots.","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The 3-loop polynomial of knots obtained by plumbing the doubles of two knots\",\"authors\":\"Kouki Yamaguchi\",\"doi\":\"10.1142/s0129167x23500866\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The 3-loop polynomial of a knot is a polynomial presenting the 3-loop part of the Kontsevich invariant of knots. In this paper, we calculate the 3-loop polynomial of knots obtained by plumbing the doubles of two knots; this class of knots includes untwisted Whitehead doubles. We construct the 3-loop polynomial by calculating the rational version of the Aarhus integral of a surgery presentation. As a consequence, we obtain an explicit presentation of the 3-loop polynomial for the knots.\",\"PeriodicalId\":54951,\"journal\":{\"name\":\"International Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0129167x23500866\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0129167x23500866","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

结的3环多项式是表示结的Kontsevich不变量的3环部分的多项式。在本文中，我们计算了通过对两个结的二重进行管道化而得到的结的三环多项式；这类绳结包括无捻怀特黑德双结。我们通过计算手术演示的奥胡斯积分的有理版本来构造3环多项式。因此，我们得到了结的3环多项式的显式表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

The 3-loop polynomial of knots obtained by plumbing the doubles of two knots

The 3-loop polynomial of a knot is a polynomial presenting the 3-loop part of the Kontsevich invariant of knots. In this paper, we calculate the 3-loop polynomial of knots obtained by plumbing the doubles of two knots; this class of knots includes untwisted Whitehead doubles. We construct the 3-loop polynomial by calculating the rational version of the Aarhus integral of a surgery presentation. As a consequence, we obtain an explicit presentation of the 3-loop polynomial for the knots.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

International Journal of Mathematics 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： The International Journal of Mathematics publishes original papers in mathematics in general, but giving a preference to those in the areas of mathematics represented by the editorial board. The journal has been published monthly except in June and December to bring out new results without delay. Occasionally, expository papers of exceptional value may also be published. The first issue appeared in March 1990.