| Title | Twisted Neumann-Zagier matrices |
| Author | |
| Corresponding Author | Garoufalidis, Stavros |
| Publication Years | 2023-12-01
|
| DOI | |
| Source Title | |
| ISSN | 2522-0144
|
| EISSN | 2197-9847
|
| Volume | 10Issue:4 |
| Abstract | The Neumann-Zagier 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 3D-index and state-integrals. We define a twisted version of Neumann-Zagier 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 1-loop invariant (a topological invariant) which determines the 1-loop 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 Neumann-Zagier matrices[J]. RESEARCH IN THE MATHEMATICAL SCIENCES,2023,10(4).
|
| APA |
Garoufalidis, Stavros,&Yoon, Seokbeom.(2023).Twisted Neumann-Zagier matrices.RESEARCH IN THE MATHEMATICAL SCIENCES,10(4).
|
| MLA |
Garoufalidis, Stavros,et al."Twisted Neumann-Zagier matrices".RESEARCH IN THE MATHEMATICAL SCIENCES 10.4(2023).
|
| Files in This Item: | There are no files associated with this item. | |||||
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