{"title":"通过 Dehn 手术获得的一些 3-manifolds的 Adjoint Reidemeister torsions","authors":"Naoko Wakijo","doi":"10.4153/s0008439524000262","DOIUrl":null,"url":null,"abstract":"<p>We determine the adjoint Reidemeister torsion of a <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240508060747903-0951:S0008439524000262:S0008439524000262_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$3$</span></span></img></span></span>-manifold obtained by some Dehn surgery along <span>K</span>, where <span>K</span> is either the figure-eight knot or the <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240508060747903-0951:S0008439524000262:S0008439524000262_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$5_2$</span></span></img></span></span>-knot. As in a vanishing conjecture (Benini et al. (2020, <span>Journal of High Energy Physics</span> 2020, 57), Gang et al. (2020, <span>Journal of High Energy Physics</span> 2020, 164), and Gang et al. (2021, <span>Advances in Theoretical and Mathematical Physics</span> 25, 1819–1845)), we consider a similar conjecture and show that the conjecture holds for the 3-manifold.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"60 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Adjoint Reidemeister torsions of some 3-manifolds obtained by Dehn surgeries\",\"authors\":\"Naoko Wakijo\",\"doi\":\"10.4153/s0008439524000262\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We determine the adjoint Reidemeister torsion of a <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240508060747903-0951:S0008439524000262:S0008439524000262_inline1.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$3$</span></span></img></span></span>-manifold obtained by some Dehn surgery along <span>K</span>, where <span>K</span> is either the figure-eight knot or the <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240508060747903-0951:S0008439524000262:S0008439524000262_inline2.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$5_2$</span></span></img></span></span>-knot. As in a vanishing conjecture (Benini et al. (2020, <span>Journal of High Energy Physics</span> 2020, 57), Gang et al. (2020, <span>Journal of High Energy Physics</span> 2020, 164), and Gang et al. (2021, <span>Advances in Theoretical and Mathematical Physics</span> 25, 1819–1845)), we consider a similar conjecture and show that the conjecture holds for the 3-manifold.</p>\",\"PeriodicalId\":501184,\"journal\":{\"name\":\"Canadian Mathematical Bulletin\",\"volume\":\"60 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-04-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Canadian Mathematical Bulletin\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4153/s0008439524000262\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Canadian Mathematical Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4153/s0008439524000262","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
我们确定了沿着 K（其中 K 是八字形结或 5_2$ 结）进行一些 Dehn 手术后得到的 3$-manifold（3$-manifold）的邻接 Reidemeister 扭转。正如一个消失猜想（贝尼尼等人（2020，《高能物理学报》，2020，57），Gang 等人（2020，《高能物理学报》，2020，164），以及 Gang 等人（2021，《理论与数学物理学进展》，25，1819-1845）），我们考虑了一个类似的猜想，并证明该猜想对 3$-manifold 成立。
Adjoint Reidemeister torsions of some 3-manifolds obtained by Dehn surgeries
We determine the adjoint Reidemeister torsion of a $3$-manifold obtained by some Dehn surgery along K, where K is either the figure-eight knot or the $5_2$-knot. As in a vanishing conjecture (Benini et al. (2020, Journal of High Energy Physics 2020, 57), Gang et al. (2020, Journal of High Energy Physics 2020, 164), and Gang et al. (2021, Advances in Theoretical and Mathematical Physics 25, 1819–1845)), we consider a similar conjecture and show that the conjecture holds for the 3-manifold.
$3$-manifold obtained by some Dehn surgery along K, where K is either the figure-eight knot or the 
$5_2$-knot. As in a vanishing conjecture (Benini et al. (2020, Journal of High Energy Physics 2020, 57), Gang et al. (2020, Journal of High Energy Physics 2020, 164), and Gang et al. (2021, Advances in Theoretical and Mathematical Physics 25, 1819–1845)), we consider a similar conjecture and show that the conjecture holds for the 3-manifold.
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