$5_2$结Kashaev不变量的渐近展开式

IF 1 2区数学 Q1 MATHEMATICS Quantum Topology Pub Date : 2016-01-01 DOI:10.4171/QT/83

T. Ohtsuki

{"title":"$5_2$结Kashaev不变量的渐近展开式","authors":"T. Ohtsuki","doi":"10.4171/QT/83","DOIUrl":null,"url":null,"abstract":"We give a presentation of the asymptotic expansion of the Kashaev invariant of the 52 knot. As the volume conjecture states, the leading term of the expansion presents the hyperbolic volume and the Chern-Simons invariant of the complement of the 52 knot. Further, we obtain a method to compute the full Poincare asymptotics to all orders of the Kashaev invariant of the 52 knot.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"66 1","pages":"669-735"},"PeriodicalIF":1.0000,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"42","resultStr":"{\"title\":\"On the asymptotic expansion of the Kashaev invariant of the $5_2$ knot\",\"authors\":\"T. Ohtsuki\",\"doi\":\"10.4171/QT/83\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give a presentation of the asymptotic expansion of the Kashaev invariant of the 52 knot. As the volume conjecture states, the leading term of the expansion presents the hyperbolic volume and the Chern-Simons invariant of the complement of the 52 knot. Further, we obtain a method to compute the full Poincare asymptotics to all orders of the Kashaev invariant of the 52 knot.\",\"PeriodicalId\":51331,\"journal\":{\"name\":\"Quantum Topology\",\"volume\":\"66 1\",\"pages\":\"669-735\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2016-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"42\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum Topology\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/QT/83\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Topology","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/QT/83","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 42

摘要

给出了52结的Kashaev不变量的渐近展开式。如体积猜想所述，展开式的首项表示双曲体积和52结补的chen - simons不变量。进一步，我们得到了52结所有阶Kashaev不变量的全Poincare渐近的一种计算方法。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

On the asymptotic expansion of the Kashaev invariant of the $5_2$ knot

We give a presentation of the asymptotic expansion of the Kashaev invariant of the 52 knot. As the volume conjecture states, the leading term of the expansion presents the hyperbolic volume and the Chern-Simons invariant of the complement of the 52 knot. Further, we obtain a method to compute the full Poincare asymptotics to all orders of the Kashaev invariant of the 52 knot.

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

Quantum Topology Mathematics-Geometry and Topology

CiteScore

1.80

自引率

9.10%

发文量

期刊介绍： Quantum Topology is a peer reviewed journal dedicated to publishing original research articles, short communications, and surveys in quantum topology and related areas of mathematics. Topics covered include in particular: Low-dimensional Topology Knot Theory Jones Polynomial and Khovanov Homology Topological Quantum Field Theory Quantum Groups and Hopf Algebras Mapping Class Groups and Teichmüller space Categorification Braid Groups and Braided Categories Fusion Categories Subfactors and Planar Algebras Contact and Symplectic Topology Topological Methods in Physics.