Twisted Neumann-Zagier matrices

Garoufalidis, Stavros1,2; Yoon, Seokbeom1

2023-12-01

10.1007/s40687-023-00400-3

RESEARCH IN THE MATHEMATICAL SCIENCES   影响因子和分区

2522-0144

2197-9847

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.

Torsion 1-loop invariant Adjoint Reidemeister torsion Infinite cyclic cover Twisted Alexander polynomial Ideal triangulations Knots Hyperbolic 3-manifolds Neumann-Zagier matrices Twisted Neumann-Zagier matrices Block circulant matrices

SCI

英语

第一 ; 通讯

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

Mathematics

Mathematics

WOS:001060258500001

SPRINGER INT PUBL AG

2-s2.0-85169907507

Web of Science

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

Garoufalidis, Stavros,Yoon, Seokbeom. Twisted Neumann-Zagier matrices[J]. RESEARCH IN THE MATHEMATICAL SCIENCES,2023,10(4).

Garoufalidis, Stavros,&Yoon, Seokbeom.(2023).Twisted Neumann-Zagier matrices.RESEARCH IN THE MATHEMATICAL SCIENCES,10(4).

Garoufalidis, Stavros,et al."Twisted Neumann-Zagier matrices".RESEARCH IN THE MATHEMATICAL SCIENCES 10.4(2023).