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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1907.06025 |
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| _version_ | 1866915964673589248 |
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| author | Breen, Joseph Christian, Austin Honda, Ko Huang, Yang |
| author_facet | Breen, Joseph Christian, Austin Honda, Ko Huang, Yang |
| contents | We lay the foundations of convex hypersurface theory in contact topology, extending the work of Giroux in dimension three. Specifically, we prove that any closed hypersurface in a contact manifold can be $C^0$-approximated by a convex one. We also prove that a $C^0$-generic family of mutually disjoint closed hypersurfaces parametrized by $t\in[0,1]$ is convex except at finitely many times $t_1,\dots,t_N$, and that crossing each $t_i$ corresponds to a bypass attachment. As an application, we prove the existence of compatible (relative) open book decompositions for contact manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_06025 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Convex hypersurface theory in contact topology Breen, Joseph Christian, Austin Honda, Ko Huang, Yang Symplectic Geometry We lay the foundations of convex hypersurface theory in contact topology, extending the work of Giroux in dimension three. Specifically, we prove that any closed hypersurface in a contact manifold can be $C^0$-approximated by a convex one. We also prove that a $C^0$-generic family of mutually disjoint closed hypersurfaces parametrized by $t\in[0,1]$ is convex except at finitely many times $t_1,\dots,t_N$, and that crossing each $t_i$ corresponds to a bypass attachment. As an application, we prove the existence of compatible (relative) open book decompositions for contact manifolds. |
| title | Convex hypersurface theory in contact topology |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/1907.06025 |