Taut polynomials from finite quotients of fibered hyperbolic 3-manifold groups
Abstract
We prove that, whenever the monodromy maps are fully-punctured, the finite quotients of a fibered hyperbolic $3$-manifold group detect the taut polynomials of the fibered faces of the Thurston norm ball, as well as the Teichmüller polynomials of suitable Dehn fillings. Toward this, we develop a general framework for the profinite invariance of twisted multivariable Alexander polynomials, which is of independent interest; we also prove that being fully-punctured and preserving transverse orientations are profinite properties of the monodromy maps. As an application, we identify specific one-cusped hyperbolic $3$-manifolds \blue{whose fundamental groups} are profinitely rigid among $3$-manifold groups, by a strategy using normalized dilatations and the veering census; notably, the taut polynomials distinguish a pair of mapping tori sharing the fiber and the dilatation.
Related
- Construction of Anosov flows on fibered hyperbolic 3-manifolds
- Cannon-Thurston Maps, Harmonic Maps, and Minimal Surfaces in Fibered Hyperbolic 3-Manifolds
- Menger Curve and Non-Planar Boundaries in Quotients of Hyperbolic Groups
- Random Quotients of Hyperbolic Spaces with Respect to WPD Actions and Linear Connectivity of the Boundary
- The hyperbolic class and vanishing laws in a TMF-valued four-manifold invariant
BibTeX
@misc{cheethamwest2026taut,
title = {{Taut polynomials from finite quotients of fibered hyperbolic 3-manifold groups}},
author = {Tamunonye Cheetham-West and Biao Ma and Jun Ueki and Youheng Yao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.21039},
eprint = {2606.21039},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.21039},
}
RIS
TY - UNPB
TI - Taut polynomials from finite quotients of fibered hyperbolic 3-manifold groups
AU - Tamunonye Cheetham-West
AU - Biao Ma
AU - Jun Ueki
AU - Youheng Yao
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2606.21039
UR - https://arxiv.org/abs/2606.21039
AB - We prove that, whenever the monodromy maps are fully-punctured, the finite quotients of a fibered hyperbolic $3$-manifold group detect the taut polynomials of the fibered faces of the Thurston norm ball, as well as the Teichmüller polynomials of suitable Dehn fillings. Toward this, we develop a general framework for the profinite invariance of twisted multivariable Alexander polynomials, which is of independent interest; we also prove that being fully-punctured and preserving transverse orientations are profinite properties of the monodromy maps. As an application, we identify specific one-cusped hyperbolic $3$-manifolds \blue{whose fundamental groups} are profinitely rigid among $3$-manifold groups, by a strategy using normalized dilatations and the veering census; notably, the taut polynomials distinguish a pair of mapping tori sharing the fiber and the dilatation.
ER -