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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.20110 |
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| _version_ | 1866909756903391232 |
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| author | Liu, Tianwei |
| author_facet | Liu, Tianwei |
| contents | This note surveys recent progress toward the profinite rigidity of orientable finite-volume hyperbolic 3-manifolds. Beginning in a brief review of some basic settings of profinite completion and rigidity of general groups, we state the complete results in profinite detection of 3-manifold decompositions and profinite rigidity or nonrigidity of other types of 3-manifolds, which reduce the problem to the hyperbolic case. Then we give some evidence to a positive answer and conclude some existing ideas toward the remained hyperbolic case. We also summarize the methods and techniques used in the process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20110 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Toward the profinite rigidity of hyperbolic 3-manifolds Liu, Tianwei Geometric Topology This note surveys recent progress toward the profinite rigidity of orientable finite-volume hyperbolic 3-manifolds. Beginning in a brief review of some basic settings of profinite completion and rigidity of general groups, we state the complete results in profinite detection of 3-manifold decompositions and profinite rigidity or nonrigidity of other types of 3-manifolds, which reduce the problem to the hyperbolic case. Then we give some evidence to a positive answer and conclude some existing ideas toward the remained hyperbolic case. We also summarize the methods and techniques used in the process. |
| title | Toward the profinite rigidity of hyperbolic 3-manifolds |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2508.20110 |