Profinite rigidity and geometric convergence
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909448043233280 |
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| author | Huang, Yu |
| author_facet | Huang, Yu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02234 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Profinite rigidity and geometric convergence Huang, Yu Geometric Topology Group Theory Primary 57M50, Secondary 57K32, 57K30 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. |
| title | Profinite rigidity and geometric convergence |
| topic | Geometric Topology Group Theory Primary 57M50, Secondary 57K32, 57K30 |
| url | https://arxiv.org/abs/2501.02234 |