{"title":"The Benard-Conway invariant of two-component links","authors":"Zedan Liu, Nikolai Saveliev","doi":"arxiv-2408.16161","DOIUrl":null,"url":null,"abstract":"The Benard-Conway invariant of links in the 3-sphere is a Casson-Lin type\ninvariant defined by counting irreducible SU(2) representations of the link\ngroup with fixed meridional traces. For two-component links with linking number\none, the invariant has been shown to equal a symmetrized multivariable link\nsignature. We extend this result to all two-component links with non-zero\nlinking number. A key ingredient in the proof is an explicit calculation of the\nBenard-Conway invariant for (2, 2l)-torus links with the help of the Chebyshev\npolynomials.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"44 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.16161","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
The Benard-Conway invariant of links in the 3-sphere is a Casson-Lin type
invariant defined by counting irreducible SU(2) representations of the link
group with fixed meridional traces. For two-component links with linking number
one, the invariant has been shown to equal a symmetrized multivariable link
signature. We extend this result to all two-component links with non-zero
linking number. A key ingredient in the proof is an explicit calculation of the
Benard-Conway invariant for (2, 2l)-torus links with the help of the Chebyshev
polynomials.
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