Cosmetic contact surgeries along transverse knots and the knot complement problem
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| _version_ | 1866912886000975872 |
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| author | Kegel, Marc |
| author_facet | Kegel, Marc |
| contents | We study cosmetic contact surgeries along transverse knots in the standard contact 3-sphere, i.e. contact surgeries that yield again the standard contact 3-sphere. The main result is that we can exclude non-trivial cosmetic contact surgeries along all transverse knots not isotopic to the transverse unknot with self-linking number -1. As a corollary it follows that every transverse knot in the standard contact 3-sphere is determined by the contactomorphism type of its exteriors. Moreover, we give counterexamples to this for transverse links in the standard contact 3-sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1703_05596 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Cosmetic contact surgeries along transverse knots and the knot complement problem Kegel, Marc Geometric Topology Symplectic Geometry 53D35 (Primary), 53D10, 57M25, 57M27, 57R65, 57N40 (Secondary) We study cosmetic contact surgeries along transverse knots in the standard contact 3-sphere, i.e. contact surgeries that yield again the standard contact 3-sphere. The main result is that we can exclude non-trivial cosmetic contact surgeries along all transverse knots not isotopic to the transverse unknot with self-linking number -1. As a corollary it follows that every transverse knot in the standard contact 3-sphere is determined by the contactomorphism type of its exteriors. Moreover, we give counterexamples to this for transverse links in the standard contact 3-sphere. |
| title | Cosmetic contact surgeries along transverse knots and the knot complement problem |
| topic | Geometric Topology Symplectic Geometry 53D35 (Primary), 53D10, 57M25, 57M27, 57R65, 57N40 (Secondary) |
| url | https://arxiv.org/abs/1703.05596 |