arXiv subjects

Tamunonye Cheetham-West

Publications and source records attributed to Tamunonye Cheetham-West.

9 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↗

arXiv2026

Profinite rigidity for two-bridge links and 3-tangle Montesinos links

For any two-bridge link or 3-tangle Montesinos link $L\subset S^3$ (including knot), this paper proves that $π_1(S^3-L)$ is profinitely rigid among the fundamental groups of compact orientable 3-manifolds.

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↗

arXiv2024

Profinite rigidity and hyperbolic four-punctured sphere bundles over the circle

We show that hyperbolic four-punctured $S^2-$bundles over $S^1$ are distinguished by the finite quotients of their fundamental groups among all 3-manifold groups. To do this, we upgrade a result of Liu to show that the topological type of a fiber is detected by the profinite completion of the fundamental group of a fibered hyperbolic 3-manifold.

math.GT↗

arXiv2024

Determining knot groups by finite quotients

We prove that hyperbolic 2-bridge knots are determined amongst all compact 3-manifolds by the profinite completions of their knot groups.

math.GT↗

arXiv2023

Characterizing candidates for Cannon's Conjecture from Geometric Measure Theory

We show that recent work of Song implies that torsion-free hyperbolic groups with Gromov boundary $S^2$ are realized as fundamental groups of closed 3-manifolds of constant negative curvature if and only if the solution to an associated spherical Plateau problem for group homology is isometric to such a 3-manifold, and suggest some related questions.

math.GT↗

arXiv2022

Property FA is not a profinite property

We exhibit infinitely many pairs of non-isomorphic finitely presented, residually finite groups $Δ$ and $Γ$ with $Δ$ having Property FA, $Γ$ having a non-trivial action on a tree and $Δ$ and $Γ$ having isomorphic profinite completions.

math.GR↗

arXiv2022

Distinguishing some genus one knots using finite quotients

We give a criterion for distinguishing a prime knot $K$ in $S^3$ from every other knot in $S^3$ using the finite quotients of $π_1(S^3\setminus K)$. Using recent work of Baldwin-Sivek, we apply this criterion to the hyperbolic knots $5_2$, $15n_{43522}$, and the three-strand pretzel knots $P(-3,3,2n+1)$ for every integer $n$.

math.GT↗

arXiv2022

Absolute profinite rigidity of some closed fibered hyperbolic 3-manifolds

We give the first examples of closed fibered hyperbolic 3-manifolds whose fundamental groups are distinguished from every other finitely generated, residually finite group by their finite quotients. One of the examples is also the first example of a non-orientable profinitely rigid hyperbolic 3-manifold.

math.GT↗