Profinite rigidity and geometric convergence

Yu Huang

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arXiv · 2501.02234

Profinite rigidity and geometric convergence

Yu Huang

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Abstract

In this paper, we prove that profinitely rigid finite-volume hyperbolic manifolds form a closed set under geometric topology. This observation implies the profinite rigidity of a large family of cusped hyperbolic manifolds via bubble-drilling construction. The core of the proof is a strong criterion that is used to verify when bubble-drilled manifolds are hyperbolic. This family includes many link complements, such as the Whitehead link complement and the Borromean ring complement.

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Yu Huang. 2025-01-04. Profinite rigidity and geometric convergence. https://arxiv.org/abs/2501.02234

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