Genericity of hyperbolic 3-manifolds via Dehn surgery

Renxing Wan; Yanqing Zou

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arXiv · 2607.11057

Genericity of hyperbolic 3-manifolds via Dehn surgery

Renxing Wan·Yanqing Zou

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Abstract

A significant result by Lickorish and Wallace shows that every closed, orientable 3-manifold can be obtained from a Dehn surgery on one link in 3-sphere. As links and Dehn surgeries vary vastly in the universe, a question arises: how can we describe their properties in vague? We introduce a counting model on links and Dehn surgeries, and prove that under this model, (1) a randon link is hyperbolic; (2) a random 3-manifold is hyperbolic.

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Renxing Wan, Yanqing Zou. 2026-07-13. Genericity of hyperbolic 3-manifolds via Dehn surgery. https://arxiv.org/abs/2607.11057

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