Maciej Borodzik, Anthony Conway, Wojciech Politarczyk
{"title":"Twisted Blanchfield pairings and twisted signatures III: Applications","authors":"Maciej Borodzik, Anthony Conway, Wojciech Politarczyk","doi":"10.1017/s0017089524000077","DOIUrl":null,"url":null,"abstract":"This paper describes how to compute algorithmically certain twisted signature invariants of a knot <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000077_inline1.png\" /> <jats:tex-math> $K$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> using twisted Blanchfield forms. An illustration of the algorithm is implemented on <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000077_inline2.png\" /> <jats:tex-math> $(2,q)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-torus knots. Additionally, using satellite formulas for these invariants, we also show how to obstruct the sliceness of certain iterated torus knots.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0017089524000077","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
This paper describes how to compute algorithmically certain twisted signature invariants of a knot $K$ using twisted Blanchfield forms. An illustration of the algorithm is implemented on $(2,q)$ -torus knots. Additionally, using satellite formulas for these invariants, we also show how to obstruct the sliceness of certain iterated torus knots.