双成分链接的贝纳德-康威不变量

arXiv - MATH - Geometric Topology Pub Date : 2024-08-28 DOI:arxiv-2408.16161

Zedan Liu, Nikolai Saveliev

{"title":"双成分链接的贝纳德-康威不变量","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":"{\"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}","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

摘要

3 球中链接的贝纳德-康威不变量是一个卡松-林型不变量，它是通过计算具有固定子午迹的链接群的不可还原 SU(2) 表示而定义的。对于链接数为一的双分量链接，已证明该不变量等于对称多变量链接特征。我们将这一结果推广到所有非连接数的双组分链接。证明中的一个关键要素是借助切比雪夫波伦二次项明确计算 (2, 2l)-torus 链接的贝纳德-康威不变量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

The Benard-Conway invariant of two-component links

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Geometric Topology

自引率

0.00%

发文量