Algebraic aspects of holomorphic quantum modular forms

An, Ni1; Garoufalidis, Stavros2,3; Li, Shana Yunsheng2

2024-09-01

10.1007/s40687-024-00464-9

RESEARCH IN THE MATHEMATICAL SCIENCES   影响因子和分区

2522-0144

2197-9847

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)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(-2,3,7)$$\end{document}-pretzel knot.

Knots Links 3-manifolds Jones polynomial Hyperbolic 3-manifolds Kauffman bracket Skein theory Witten's conjecture Habiro ring Quantum modularity conjecture Volume conjecture Faddeev quantum dilogarithm State integrals Holomorphic quantum modular forms

SCI

英语

第一 ; 通讯

Mathematics

Mathematics

WOS:001283954600001

SPRINGER INT PUBL AG

Web of Science

1.Southern Univ Sci & Technol, Dept Math, Shenzhen, Peoples R China
2.Southern Univ Sci & Technol, Int Ctr Math, Dept Math, Shenzhen, Peoples R China
3.Max Planck Inst Math, Bonn, Germany

An, Ni,Garoufalidis, Stavros,Li, Shana Yunsheng. Algebraic aspects of holomorphic quantum modular forms[J]. RESEARCH IN THE MATHEMATICAL SCIENCES,2024,11(3).

An, Ni,Garoufalidis, Stavros,&Li, Shana Yunsheng.(2024).Algebraic aspects of holomorphic quantum modular forms.RESEARCH IN THE MATHEMATICAL SCIENCES,11(3).

An, Ni,et al."Algebraic aspects of holomorphic quantum modular forms".RESEARCH IN THE MATHEMATICAL SCIENCES 11.3(2024).