全形量子模态的代数方面

IF 1.2 3区数学 Q1 MATHEMATICS Research in the Mathematical Sciences Pub Date : 2024-08-05 DOI:10.1007/s40687-024-00464-9

Ni An, Stavros Garoufalidis, Shana Yunsheng Li

{"title":"全形量子模态的代数方面","authors":"Ni An, Stavros Garoufalidis, Shana Yunsheng Li","doi":"10.1007/s40687-024-00464-9","DOIUrl":null,"url":null,"abstract":"Matrix-valued holomorphic quantum modular forms are intricate objects associated to 3-manifolds (in particular to knot complements) that arise in successive refinements of the volume conjecture of knots and involve three holomorphic, asymptotic and arithmetic realizations. It is expected that the algebraic properties of these objects can be deduced from the algebraic properties of descendant state integrals, and we illustrate this for the case of the \\((-2,3,7)\\)-pretzel knot.","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Algebraic aspects of holomorphic quantum modular forms\",\"authors\":\"Ni An, Stavros Garoufalidis, Shana Yunsheng Li\",\"doi\":\"10.1007/s40687-024-00464-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Matrix-valued holomorphic quantum modular forms are intricate objects associated to 3-manifolds (in particular to knot complements) that arise in successive refinements of the volume conjecture of knots and involve three holomorphic, asymptotic and arithmetic realizations. It is expected that the algebraic properties of these objects can be deduced from the algebraic properties of descendant state integrals, and we illustrate this for the case of the \\\\((-2,3,7)\\\\)-pretzel knot.\",\"PeriodicalId\":48561,\"journal\":{\"name\":\"Research in the Mathematical Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-08-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Research in the Mathematical Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s40687-024-00464-9\",\"RegionNum\":3,\"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":"Research in the Mathematical Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40687-024-00464-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

矩阵值全形量子模形式是与三芒星（特别是结的补集）相关的复杂对象，它出现在结的体积猜想的连续细化中，涉及三种全形、渐近和算术实现。预计这些对象的代数性质可以从子态积分的代数性质中推导出来，我们以 \((-2,3,7)\)-pretzel 结为例加以说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

摘要图片

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Algebraic aspects of holomorphic quantum modular forms

Matrix-valued holomorphic quantum modular forms are intricate objects associated to 3-manifolds (in particular to knot complements) that arise in successive refinements of the volume conjecture of knots and involve three holomorphic, asymptotic and arithmetic realizations. It is expected that the algebraic properties of these objects can be deduced from the algebraic properties of descendant state integrals, and we illustrate this for the case of the \((-2,3,7)\)-pretzel 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

Research in the Mathematical Sciences Mathematics-Computational Mathematics

CiteScore

2.00

自引率

8.30%

发文量

期刊介绍： Research in the Mathematical Sciences is an international, peer-reviewed hybrid journal covering the full scope of Theoretical Mathematics, Applied Mathematics, and Theoretical Computer Science. The Mission of the Journal is to publish high-quality original articles that make a significant contribution to the research areas of both theoretical and applied mathematics and theoretical computer science. This journal is an efficient enterprise where the editors play a central role in soliciting the best research papers, and where editorial decisions are reached in a timely fashion. Research in the Mathematical Sciences does not have a length restriction and encourages the submission of longer articles in which more complex and detailed analysis and proofing of theorems is required. It also publishes shorter research communications (Letters) covering nascent research in some of the hottest areas of mathematical research. This journal will publish the highest quality papers in all of the traditional areas of applied and theoretical areas of mathematics and computer science, and it will actively seek to publish seminal papers in the most emerging and interdisciplinary areas in all of the mathematical sciences. Research in the Mathematical Sciences wishes to lead the way by promoting the highest quality research of this type.

期刊最新文献

Proceedings of the 17th International Workshop on Real and Complex Singularities Splitting hypergeometric functions over roots of unity Evaluations and relations for finite trigonometric sums Tropical adic spaces I: the continuous spectrum of a topological semiring Algebraic aspects of holomorphic quantum modular forms