Contact surgery numbers of Sigma(2,3,11) and L(4m+3,4)
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910426520879104 |
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| author | Chatterjee, Rima Kegel, Marc |
| author_facet | Chatterjee, Rima Kegel, Marc |
| contents | We classify all contact structures with contact surgery number one on the Brieskorn sphere Sigma(2,3,11) with both orientations. We conclude that there exist infinitely many non-isotopic contact structures on each of the above manifolds which cannot be obtained by a single rational contact surgery from the standard tight contact 3-sphere. We further prove similar results for some lens spaces: We classify all contact structures with contact surgery number one on lens spaces of the form L(4m+3,4). Along the way, we present an algorithm and a formula for computing the Euler class of a contact structure from a general rational contact surgery description and classify which rational surgeries along Legendrian unknots are tight and which ones are overtwisted. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18177 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Contact surgery numbers of Sigma(2,3,11) and L(4m+3,4) Chatterjee, Rima Kegel, Marc Symplectic Geometry Geometric Topology 53D35, 53D10, 57K10, 57R65, 57K10, 57K33 We classify all contact structures with contact surgery number one on the Brieskorn sphere Sigma(2,3,11) with both orientations. We conclude that there exist infinitely many non-isotopic contact structures on each of the above manifolds which cannot be obtained by a single rational contact surgery from the standard tight contact 3-sphere. We further prove similar results for some lens spaces: We classify all contact structures with contact surgery number one on lens spaces of the form L(4m+3,4). Along the way, we present an algorithm and a formula for computing the Euler class of a contact structure from a general rational contact surgery description and classify which rational surgeries along Legendrian unknots are tight and which ones are overtwisted. |
| title | Contact surgery numbers of Sigma(2,3,11) and L(4m+3,4) |
| topic | Symplectic Geometry Geometric Topology 53D35, 53D10, 57K10, 57R65, 57K10, 57K33 |
| url | https://arxiv.org/abs/2404.18177 |