Maciej Borodzik, Anthony Conway, Wojciech Politarczyk
{"title":"扭曲布兰奇菲尔德配对和扭曲签名 III:应用","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":"{\"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}","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}
Twisted Blanchfield pairings and twisted signatures III: Applications
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.