Lorena Armas-Sanabria , Jesús Rodríguez Viorato , E. Fanny Jasso-Hernández
{"title":"三元组和双曲封闭纯三元组的阿尔廷呈现","authors":"Lorena Armas-Sanabria , Jesús Rodríguez Viorato , E. Fanny Jasso-Hernández","doi":"10.1016/j.topol.2024.108989","DOIUrl":null,"url":null,"abstract":"<div><p>We consider a special class of framed links that arise from the hexatangle. Such links are introduced in <span>[3]</span>, where it was also analyzed when the 3-manifold obtained after performing integral Dehn surgery on closed pure 3-braids is <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. In the present paper, we analyze the symmetries of the hexatangle and give a list of Artin <em>n</em>-presentations for the trivial group. These presentations correspond to the double-branched covers of the hexatangle that produce <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> after Dehn surgery. Also, using a result of Birman and Menasco <span>[4]</span>, we determine which closed pure 3-braids are hyperbolic.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"354 ","pages":"Article 108989"},"PeriodicalIF":0.6000,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Artin presentations of the trivial group and hyperbolic closed pure 3-braids\",\"authors\":\"Lorena Armas-Sanabria , Jesús Rodríguez Viorato , E. Fanny Jasso-Hernández\",\"doi\":\"10.1016/j.topol.2024.108989\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider a special class of framed links that arise from the hexatangle. Such links are introduced in <span>[3]</span>, where it was also analyzed when the 3-manifold obtained after performing integral Dehn surgery on closed pure 3-braids is <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. In the present paper, we analyze the symmetries of the hexatangle and give a list of Artin <em>n</em>-presentations for the trivial group. These presentations correspond to the double-branched covers of the hexatangle that produce <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> after Dehn surgery. Also, using a result of Birman and Menasco <span>[4]</span>, we determine which closed pure 3-braids are hyperbolic.</p></div>\",\"PeriodicalId\":51201,\"journal\":{\"name\":\"Topology and its Applications\",\"volume\":\"354 \",\"pages\":\"Article 108989\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-06-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topology and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0166864124001743\",\"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":"Topology and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166864124001743","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Artin presentations of the trivial group and hyperbolic closed pure 3-braids
We consider a special class of framed links that arise from the hexatangle. Such links are introduced in [3], where it was also analyzed when the 3-manifold obtained after performing integral Dehn surgery on closed pure 3-braids is . In the present paper, we analyze the symmetries of the hexatangle and give a list of Artin n-presentations for the trivial group. These presentations correspond to the double-branched covers of the hexatangle that produce after Dehn surgery. Also, using a result of Birman and Menasco [4], we determine which closed pure 3-braids are hyperbolic.
期刊介绍：
Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology.
At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.
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