{"title":"关于辫状和链状的链同伦","authors":"Emmanuel Graff","doi":"10.2969/jmsj/90449044","DOIUrl":null,"url":null,"abstract":"This paper deals with links and braids up to link-homotopy, studied from the viewpoint of Habiro's clasper calculus. More precisely, we use clasper homotopy calculus in two main directions. First, we define and compute a faithful linear representation of the homotopy braid group, by using claspers as geometric commutators. Second, we give a geometric proof of Levine's classification of 4-component links up to link-homotopy, and go further with the classification of 5-component links in the algebraically split case.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2022-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On braids and links up to link-homotopy\",\"authors\":\"Emmanuel Graff\",\"doi\":\"10.2969/jmsj/90449044\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper deals with links and braids up to link-homotopy, studied from the viewpoint of Habiro's clasper calculus. More precisely, we use clasper homotopy calculus in two main directions. First, we define and compute a faithful linear representation of the homotopy braid group, by using claspers as geometric commutators. Second, we give a geometric proof of Levine's classification of 4-component links up to link-homotopy, and go further with the classification of 5-component links in the algebraically split case.\",\"PeriodicalId\":49988,\"journal\":{\"name\":\"Journal of the Mathematical Society of Japan\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-10-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Mathematical Society of Japan\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2969/jmsj/90449044\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Mathematical Society of Japan","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2969/jmsj/90449044","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
This paper deals with links and braids up to link-homotopy, studied from the viewpoint of Habiro's clasper calculus. More precisely, we use clasper homotopy calculus in two main directions. First, we define and compute a faithful linear representation of the homotopy braid group, by using claspers as geometric commutators. Second, we give a geometric proof of Levine's classification of 4-component links up to link-homotopy, and go further with the classification of 5-component links in the algebraically split case.
期刊介绍：
The Journal of the Mathematical Society of Japan (JMSJ) was founded in 1948 and is published quarterly by the Mathematical Society of Japan (MSJ). It covers a wide range of pure mathematics. To maintain high standards, research articles in the journal are selected by the editorial board with the aid of distinguished international referees. Electronic access to the articles is offered through Project Euclid and J-STAGE. We provide free access to back issues three years after publication (available also at Online Index).
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