Title  Twisted NeumannZagier matrices 
Author  
Corresponding Author  Garoufalidis, Stavros 
Publication Years  20231201

DOI  
Source Title  
ISSN  25220144

EISSN  21979847

Volume  10Issue:4 
Abstract  The NeumannZagier matrices of an ideal triangulation are integer matrices with symplectic properties whose entries encode the number of tetrahedra that wind around each edge of the triangulation. They can be used as input data for the construction of a number of quantum invariants that include the loop invariants, the 3Dindex and stateintegrals. We define a twisted version of NeumannZagier matrices, describe their symplectic properties, and show how to compute them from the combinatorics of an ideal triangulation. As a sample application, we use them to define a twisted version of the 1loop invariant (a topological invariant) which determines the 1loop invariant of the cyclic covers of a hyperbolic knot complement, and conjecturally is equal to the adjoint twisted Alexander polynomial. 
Keywords  
URL  [Source Record] 
Indexed By  
Language  English

SUSTech Authorship  First
; Corresponding

Funding Project  Basic Science Research Program through the NRF of Korea  Ministry of Education[2020R1A6A3A03037901]

WOS Research Area  Mathematics

WOS Subject  Mathematics

WOS Accession No  WOS:001060258500001

Publisher  
Data Source  Web of Science

Citation statistics 
Cited Times [WOS]:0

Document Type  Journal Article 
Identifier  http://kc.sustech.edu.cn/handle/2SGJ60CL/559336 
Department  Department of Mathematics 
Affiliation  1.Southern Univ Sci & Technol, Int Ctr Math, Dept Math, Shenzhen, Peoples R China 2.Max Planck Inst Math, Bonn, Germany 
First Author Affilication  Department of Mathematics 
Corresponding Author Affilication  Department of Mathematics 
First Author's First Affilication  Department of Mathematics 
Recommended Citation GB/T 7714 
Garoufalidis, Stavros,Yoon, Seokbeom. Twisted NeumannZagier matrices[J]. RESEARCH IN THE MATHEMATICAL SCIENCES,2023,10(4).

APA 
Garoufalidis, Stavros,&Yoon, Seokbeom.(2023).Twisted NeumannZagier matrices.RESEARCH IN THE MATHEMATICAL SCIENCES,10(4).

MLA 
Garoufalidis, Stavros,et al."Twisted NeumannZagier matrices".RESEARCH IN THE MATHEMATICAL SCIENCES 10.4(2023).

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