Contact surgery numbers of projective spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914312833990656 |
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| author | Kegel, Marc Yadav, Monika |
| author_facet | Kegel, Marc Yadav, Monika |
| contents | We classify all contact projective spaces with contact surgery number one. In particular, this implies that there exist infinitely many non-isotopic contact structures on the real projective 3-space which cannot be obtained by a single rational contact surgery from the standard tight contact 3-sphere.
Large parts of our proofs deal with a detailed analysis of Gompf's $Γ$-invariant of tangential 2-plane fields on 3-manifolds. From our main result we also deduce that the $Γ$-invariant of a tangential 2-plane field on the real projective 3-space only depends on its $d_3$-invariant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05032 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Contact surgery numbers of projective spaces Kegel, Marc Yadav, Monika Geometric Topology Symplectic Geometry 53D35, 53D10, 57K10, 57R65, 57K10, 57K33 We classify all contact projective spaces with contact surgery number one. In particular, this implies that there exist infinitely many non-isotopic contact structures on the real projective 3-space which cannot be obtained by a single rational contact surgery from the standard tight contact 3-sphere. Large parts of our proofs deal with a detailed analysis of Gompf's $Γ$-invariant of tangential 2-plane fields on 3-manifolds. From our main result we also deduce that the $Γ$-invariant of a tangential 2-plane field on the real projective 3-space only depends on its $d_3$-invariant. |
| title | Contact surgery numbers of projective spaces |
| topic | Geometric Topology Symplectic Geometry 53D35, 53D10, 57K10, 57R65, 57K10, 57K33 |
| url | https://arxiv.org/abs/2504.05032 |