On the Profinite Distinguishability of Hyperbolic Dehn Fillings of Finite-Volume 3-Manifolds

We use model theory to study relative profinite rigidity of 3-manifold groups and show that given any residually finite group Γ with finite character variety and single-cusped finite volume hyperbolic 3-manifold M, cofinitely many Dehn fillings M_p/q are profinitely distinguishable from Γ.