Profinite rigid hyperbolic 3-manifolds are closed under geometric convergence, and bubble-drilled examples including the Whitehead link and Borromean rings are profinitely rigid.
Profinite rigidity and hyperbolic four-punctured sphere bundles over the circle
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abstract
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.
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Profinite rigidity and geometric convergence
Profinite rigid hyperbolic 3-manifolds are closed under geometric convergence, and bubble-drilled examples including the Whitehead link and Borromean rings are profinitely rigid.