The Giroux Correspondence in dimension 3
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912910615248896 |
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| author | Licata, Joan Scharitzer, Matthias Vértesi, Vera |
| author_facet | Licata, Joan Scharitzer, Matthias Vértesi, Vera |
| contents | This paper proves the Giroux Correspondence in dimension three using Heegaard splittings of contact manifolds. In two of the authors earlier paper they proved the Giroux Correspondence for tight contact 3-manifolds via convex Heegaard surfaces, and simultaneously, Honda, Breen and Huang gave an alldimensions proof of the Giroux Correspondence by generalising convex surface theory to higher dimensions. This paper extends the Heegaard splitting approach to arbitrary (not necessarily tight) contact 3-manifolds in order to provide a proof accessible to a low-dimensional audience. The proof assumes classification moves relating bypass decompositions for isotopic contact structures on cobordisms that are topological products; in the Appendix, we prove this result in the 3- dimensional setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01079 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Giroux Correspondence in dimension 3 Licata, Joan Scharitzer, Matthias Vértesi, Vera Geometric Topology 57K33 This paper proves the Giroux Correspondence in dimension three using Heegaard splittings of contact manifolds. In two of the authors earlier paper they proved the Giroux Correspondence for tight contact 3-manifolds via convex Heegaard surfaces, and simultaneously, Honda, Breen and Huang gave an alldimensions proof of the Giroux Correspondence by generalising convex surface theory to higher dimensions. This paper extends the Heegaard splitting approach to arbitrary (not necessarily tight) contact 3-manifolds in order to provide a proof accessible to a low-dimensional audience. The proof assumes classification moves relating bypass decompositions for isotopic contact structures on cobordisms that are topological products; in the Appendix, we prove this result in the 3- dimensional setting. |
| title | The Giroux Correspondence in dimension 3 |
| topic | Geometric Topology 57K33 |
| url | https://arxiv.org/abs/2408.01079 |