Negative contact surgery on Legendrian non-simple knots
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915895679385600 |
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| author | Wan, Shunyu Zhou, Hugo |
| author_facet | Wan, Shunyu Zhou, Hugo |
| contents | We prove that for any pair of Legendrian representatives of the Chekanov-Eliashberg twist knots with different LOSS invariants, any negative rational contact $r$-surgery with $r\neq -1$ always gives rise to different contact 3-manifolds distinguished by their contact invariants. This gives the first examples of pairs of Legendrian knots with the same classical invariants but distinct contact $r$-surgeries for all negative rational number $r$. We also generalize the statement from the twist knots to a certain families of two-bridge knots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00855 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Negative contact surgery on Legendrian non-simple knots Wan, Shunyu Zhou, Hugo Geometric Topology We prove that for any pair of Legendrian representatives of the Chekanov-Eliashberg twist knots with different LOSS invariants, any negative rational contact $r$-surgery with $r\neq -1$ always gives rise to different contact 3-manifolds distinguished by their contact invariants. This gives the first examples of pairs of Legendrian knots with the same classical invariants but distinct contact $r$-surgeries for all negative rational number $r$. We also generalize the statement from the twist knots to a certain families of two-bridge knots. |
| title | Negative contact surgery on Legendrian non-simple knots |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2405.00855 |