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

2025/06/14 by Tamunonye Cheetham‐West, Cheetham-West, Tamunonye, Youheng Yao +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2506.12289

openalex publication_date 2025/06/14 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• An invitation to Culler-Shalen theory in arbitrary characteristic
• Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups
• Hyperbolic 3-Manifolds Groups are Subgroup Conjugacy Separable
• On finitely generated profinite groups I: strong completeness and uniform bounds
• Boundary slopes and the logarithmic limit set

Cited by

• On regularity of profinite isomorphisms between cusped hyperbolic 3-manifolds and the A-polynomial

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