{"title":"双切片连杆的阿贝尔不变量","authors":"Anthony Conway, P. Orson","doi":"10.4171/lem/1029","DOIUrl":null,"url":null,"abstract":"We provide obstructions to a link in S3 arising as the cross section of any number of unlinked spheres in S4. Our obstructions arise from the multivariable signature, the Blanchfield form and generalised Seifert matrices. We also obtain obstructions in the case of surfaces of higher genera, leading to a lower bound on the doubly slice genus of links.","PeriodicalId":344085,"journal":{"name":"L’Enseignement Mathématique","volume":"24 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Abelian invariants of doubly slice links\",\"authors\":\"Anthony Conway, P. Orson\",\"doi\":\"10.4171/lem/1029\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We provide obstructions to a link in S3 arising as the cross section of any number of unlinked spheres in S4. Our obstructions arise from the multivariable signature, the Blanchfield form and generalised Seifert matrices. We also obtain obstructions in the case of surfaces of higher genera, leading to a lower bound on the doubly slice genus of links.\",\"PeriodicalId\":344085,\"journal\":{\"name\":\"L’Enseignement Mathématique\",\"volume\":\"24 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-01-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"L’Enseignement Mathématique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/lem/1029\",\"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/1029","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We provide obstructions to a link in S3 arising as the cross section of any number of unlinked spheres in S4. Our obstructions arise from the multivariable signature, the Blanchfield form and generalised Seifert matrices. We also obtain obstructions in the case of surfaces of higher genera, leading to a lower bound on the doubly slice genus of links.
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