{"title":"卫星链路隧道系统解结研究","authors":"D. Girão, J. Nogueira, António Salgueiro","doi":"10.2140/agt.2022.22.307","DOIUrl":null,"url":null,"abstract":"We prove that the tunnel number of a satellite chain link with a number of components higher than or equal to twice the bridge number of the companion is as small as possible among links with the same number of components. We prove this result to be sharp for satellite chain links over a 2-bridge knot. We also observe that the links in the main result satisfy the genus versus rank conjecture.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"44 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On unknotting tunnel systems of satellite chain links\",\"authors\":\"D. Girão, J. Nogueira, António Salgueiro\",\"doi\":\"10.2140/agt.2022.22.307\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that the tunnel number of a satellite chain link with a number of components higher than or equal to twice the bridge number of the companion is as small as possible among links with the same number of components. We prove this result to be sharp for satellite chain links over a 2-bridge knot. We also observe that the links in the main result satisfy the genus versus rank conjecture.\",\"PeriodicalId\":50826,\"journal\":{\"name\":\"Algebraic and Geometric Topology\",\"volume\":\"44 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-04-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebraic and Geometric Topology\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2140/agt.2022.22.307\",\"RegionNum\":3,\"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":"Algebraic and Geometric Topology","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2140/agt.2022.22.307","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
On unknotting tunnel systems of satellite chain links
We prove that the tunnel number of a satellite chain link with a number of components higher than or equal to twice the bridge number of the companion is as small as possible among links with the same number of components. We prove this result to be sharp for satellite chain links over a 2-bridge knot. We also observe that the links in the main result satisfy the genus versus rank conjecture.
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