arXiv subjects

Youheng Yao

Publications and source records attributed to Youheng Yao.

3 recordsLinked to original sources

arXiv2026

Taut polynomials from finite quotients of fibered hyperbolic 3-manifold groups

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.

math.GT↗

arXiv2025

Finite covers and strict boundary slopes of cusped hyperbolic 3-manifolds

We prove that if two cusped hyperbolic $3$-manifolds admit a regular isomorphism between the profinite completions of their fundamental groups, then they share the same $A$-polynomial and their strongly detected boundary slopes match up.

math.GT↗

arXiv2022

On the topology of character varieties of once-punctured torus bundles

This paper presents, for the special case of once-punctured torus bundles, a natural method to study the character varieties of hyperbolic 3-manifolds that are bundles over the circle. The main strategy is to restrict characters to the fibre of the bundle, and to analyse the resulting branched covering map. This allows us to extend results of Steven Boyer, Erhard Luft and Xingru Zhang. Both $SL(2, \mathbb{C})$-character varieties and $PSL(2, \mathbb{C})$-character varieties are considered. As an explicit application of these methods, we build on work of Baker and Petersen to show that there is an infinite family of hyperbolic once-punctured bundles with canonical curves of $PSL(2, \mathbb{C})$-characters of unbounded genus.

math.GT↗