Excluding cosmetic surgeries on hyperbolic 3-manifolds
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912729118277632 |
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| author | Futer, David Purcell, Jessica S. Schleimer, Saul |
| author_facet | Futer, David Purcell, Jessica S. Schleimer, Saul |
| contents | This paper employs knot invariants and results from hyperbolic geometry to develop a practical procedure for checking the cosmetic surgery conjecture on any given one-cusped manifold. This procedure has been used to establish the following computational results. First, we verify that all knots up to 19 crossings, and all one-cusped 3-manifolds in the SnapPy census, do not admit any purely cosmetic surgeries. Second, we check that a hyperbolic knot with at most 15 crossings only admits chirally cosmetic surgeries when the knot itself is amphicheiral. Third, we enumerate all knots up to 13 crossings that share a common Dehn fillings with the figure-8 knot. The code that verifies these results is publicly available on GitHub. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10448 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Excluding cosmetic surgeries on hyperbolic 3-manifolds Futer, David Purcell, Jessica S. Schleimer, Saul Geometric Topology 57K32, 57K10, 57-04, 57-08 This paper employs knot invariants and results from hyperbolic geometry to develop a practical procedure for checking the cosmetic surgery conjecture on any given one-cusped manifold. This procedure has been used to establish the following computational results. First, we verify that all knots up to 19 crossings, and all one-cusped 3-manifolds in the SnapPy census, do not admit any purely cosmetic surgeries. Second, we check that a hyperbolic knot with at most 15 crossings only admits chirally cosmetic surgeries when the knot itself is amphicheiral. Third, we enumerate all knots up to 13 crossings that share a common Dehn fillings with the figure-8 knot. The code that verifies these results is publicly available on GitHub. |
| title | Excluding cosmetic surgeries on hyperbolic 3-manifolds |
| topic | Geometric Topology 57K32, 57K10, 57-04, 57-08 |
| url | https://arxiv.org/abs/2403.10448 |