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

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arxiv 2308.00266 v3 pith:HLIMLKCM submitted 2023-08-01 math.GT math.GR

Tamunonye Cheetham-West This is my paper · ORCID
classification math.GTmath.GR
keywords hyperbolicbundlesfour-puncturedfundamentalgroupsmanifoldprofinitecircle
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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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  1. Profinite rigidity and geometric convergence

    math.GT 2025-01 conditional novelty 7.0 of 10

    Profinite rigid hyperbolic 3-manifolds are closed under geometric convergence, and bubble-drilled examples including the Whitehead link and Borromean rings are profinitely rigid.

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