$C^0$-Contact Geometry of Surfaces in 3-Manifolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909766717014016 |
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| author | Serraille, Baptiste Stokić, Maksim |
| author_facet | Serraille, Baptiste Stokić, Maksim |
| contents | We prove that contact homeomorphisms preserve characteristic foliations on surfaces in contact $3$-manifolds. More precisely, since the characteristic foliation is a singular $1$-dimensional foliation, we show that singular points are mapped to singular points, and that the image of every $1$-dimensional leaf is again a $1$-dimensional leaf in the image surface. As a consequence, regular coisotropic surfaces are $C^0$-rigid. In contrast, we show that contact convexity is $C^0$-flexible by constructing a contact homeomorphism that sends a convex $2$-torus to a non-convex one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02430 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $C^0$-Contact Geometry of Surfaces in 3-Manifolds Serraille, Baptiste Stokić, Maksim Symplectic Geometry 53D10 We prove that contact homeomorphisms preserve characteristic foliations on surfaces in contact $3$-manifolds. More precisely, since the characteristic foliation is a singular $1$-dimensional foliation, we show that singular points are mapped to singular points, and that the image of every $1$-dimensional leaf is again a $1$-dimensional leaf in the image surface. As a consequence, regular coisotropic surfaces are $C^0$-rigid. In contrast, we show that contact convexity is $C^0$-flexible by constructing a contact homeomorphism that sends a convex $2$-torus to a non-convex one. |
| title | $C^0$-Contact Geometry of Surfaces in 3-Manifolds |
| topic | Symplectic Geometry 53D10 |
| url | https://arxiv.org/abs/2509.02430 |