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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2207.12055 |
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| _version_ | 1866917861688082432 |
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| author | Cardona, Robert Oms, Cédric |
| author_facet | Cardona, Robert Oms, Cédric |
| contents | A $b$-contact structure on a $b$-manifold $(M,Z)$ is a Jacobi structure on $M$ satisfying a transversality condition along the hypersurface $Z$. We show that, in three dimensions, $b$-contact structures with overtwisted three-dimensional leaves satisfy an existence $h$-principle that allows prescribing the induced singular foliation. We give a method to classify $b$-contact structures on a given $b$-manifold and use it to give a classification on $S^3$ with either a two-sphere or an unknotted torus as the critical surface. We also discuss generalizations to higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_12055 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Existence and classification of $b$-contact structures Cardona, Robert Oms, Cédric Symplectic Geometry Differential Geometry A $b$-contact structure on a $b$-manifold $(M,Z)$ is a Jacobi structure on $M$ satisfying a transversality condition along the hypersurface $Z$. We show that, in three dimensions, $b$-contact structures with overtwisted three-dimensional leaves satisfy an existence $h$-principle that allows prescribing the induced singular foliation. We give a method to classify $b$-contact structures on a given $b$-manifold and use it to give a classification on $S^3$ with either a two-sphere or an unknotted torus as the critical surface. We also discuss generalizations to higher dimensions. |
| title | Existence and classification of $b$-contact structures |
| topic | Symplectic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2207.12055 |