An algorithm for finding minimal volume hyperbolic links and the Dehn parental test
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910863971057664 |
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| author | Schmalian, Misha |
| author_facet | Schmalian, Misha |
| contents | We describe an algorithm that, given a 3-manifold M, outputs a finite set containing all minimal volume k-component hyperbolic link complements in M. A key step, that might be of independent interest, is an algorithm that, given two 3-manifolds N and M, decides whether they are related by Dehn filling. In fact, we show that the set of boundary slopes giving a Dehn filling of N to M is determined by a special class of well-studied quadratic Diophantine (in)equalities, for which solvability is known to be decidable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05671 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An algorithm for finding minimal volume hyperbolic links and the Dehn parental test Schmalian, Misha Geometric Topology 57K32, 57-08, 57K10 We describe an algorithm that, given a 3-manifold M, outputs a finite set containing all minimal volume k-component hyperbolic link complements in M. A key step, that might be of independent interest, is an algorithm that, given two 3-manifolds N and M, decides whether they are related by Dehn filling. In fact, we show that the set of boundary slopes giving a Dehn filling of N to M is determined by a special class of well-studied quadratic Diophantine (in)equalities, for which solvability is known to be decidable. |
| title | An algorithm for finding minimal volume hyperbolic links and the Dehn parental test |
| topic | Geometric Topology 57K32, 57-08, 57K10 |
| url | https://arxiv.org/abs/2503.05671 |