{"title":"用单捻解开","authors":"S. Allen, C. Livingston","doi":"10.4171/LEM/66-3/4-10","DOIUrl":null,"url":null,"abstract":"Given a knot in the three-sphere, is it possible to unknot it by performing a single twist, and if so, what are the possible linking numbers of such a twist? We develop obstructions to unknotting using a twist of a specified linking number. The obstructions we describe are built using classical knot invariants, Casson-Gordon invariants, and Heegaard Floer theory.","PeriodicalId":344085,"journal":{"name":"L’Enseignement Mathématique","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Unknotting with a single twist\",\"authors\":\"S. Allen, C. Livingston\",\"doi\":\"10.4171/LEM/66-3/4-10\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given a knot in the three-sphere, is it possible to unknot it by performing a single twist, and if so, what are the possible linking numbers of such a twist? We develop obstructions to unknotting using a twist of a specified linking number. The obstructions we describe are built using classical knot invariants, Casson-Gordon invariants, and Heegaard Floer theory.\",\"PeriodicalId\":344085,\"journal\":{\"name\":\"L’Enseignement Mathématique\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-05-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"L’Enseignement Mathématique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/LEM/66-3/4-10\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"L’Enseignement Mathématique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/LEM/66-3/4-10","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Given a knot in the three-sphere, is it possible to unknot it by performing a single twist, and if so, what are the possible linking numbers of such a twist? We develop obstructions to unknotting using a twist of a specified linking number. The obstructions we describe are built using classical knot invariants, Casson-Gordon invariants, and Heegaard Floer theory.
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