Adjoint Reidemeister torsion from hyperbolic gluing equations
Abstract
Motivated by the study of asymptotics of quantum invariants, Dimofte and Garoufalidis introduced a power series associated to a suitable ideal triangulation of a cusped hyperbolic $3$-manifold. They proved that its constant term can be written in terms of Neumann-Zagier data and the complex shape parameters of ideal tetrahedra, and conjectured that it equals the adjoint twisted Reidemeister torsion. On the other hand, in the study of asymptotics of Turaev-Viro type invariants of cusped $ 3$-manifolds, the authors, together with Liu, Sun and Yang, found that the one-loop terms of their asymptotic expansions could be written in terms of Gram matrices and decorated edge lengths of ideal tetrahedra. In this paper, we prove the conjecture of Dimofte and Garoufalidis and relate the one-loop term appearing in the Turaev-Viro type invariant to the adjoint twisted Reidemeister torsion.
Related
- Initial Data Gluing for Asymptotically Hyperbolic Spacetimes
- Uniform small cancellation in torsion-free hyperbolic groups
- Power convexity of the torsion function on horo-convex domains in hyperbolic space
- Spectral Reconstruction of Hyperbolic Geometry as a Topological Invariant of a Self‑Adjoint Operator
- Haagerup-Izumi modular data from hyperbolic words: S-fold TQFTs, central charge, torsion and the Bethe vacua
BibTeX
@misc{ming2026adjoint,
title = {{Adjoint Reidemeister torsion from hyperbolic gluing equations}},
author = {Shuang Ming and Baojun Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29299},
eprint = {2609.29299},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29299},
}
RIS
TY - UNPB
TI - Adjoint Reidemeister torsion from hyperbolic gluing equations
AU - Shuang Ming
AU - Baojun Wu
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29299
UR - https://arxiv.org/abs/2609.29299
AB - Motivated by the study of asymptotics of quantum invariants, Dimofte and Garoufalidis introduced a power series associated to a suitable ideal triangulation of a cusped hyperbolic $3$-manifold. They proved that its constant term can be written in terms of Neumann-Zagier data and the complex shape parameters of ideal tetrahedra, and conjectured that it equals the adjoint twisted Reidemeister torsion. On the other hand, in the study of asymptotics of Turaev-Viro type invariants of cusped $ 3$-manifolds, the authors, together with Liu, Sun and Yang, found that the one-loop terms of their asymptotic expansions could be written in terms of Gram matrices and decorated edge lengths of ideal tetrahedra. In this paper, we prove the conjecture of Dimofte and Garoufalidis and relate the one-loop term appearing in the Turaev-Viro type invariant to the adjoint twisted Reidemeister torsion.
ER -