Cylindrical contact homology for weakly convex contact forms in dimension three
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908924565782528 |
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| author | de Oliveira, Ana Kelly Salomão, Pedro A. S. |
| author_facet | de Oliveira, Ana Kelly Salomão, Pedro A. S. |
| contents | A contact form $λ$ on a closed contact three-manifold $(M,ξ)$ is called weakly convex if either it has no contractible Reeb orbit, or the first Chern class of $ξ$ vanishes on $π_2(M)$, and the index of every contractible Reeb orbit is at least $2$. We present conditions for a weakly convex contact form to admit a well-defined cylindrical contact homology. The key point is a cancellation mechanism for boundary degenerations involving index-2 Reeb orbits, based on a parity property of holomorphic planes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29352 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cylindrical contact homology for weakly convex contact forms in dimension three de Oliveira, Ana Kelly Salomão, Pedro A. S. Symplectic Geometry A contact form $λ$ on a closed contact three-manifold $(M,ξ)$ is called weakly convex if either it has no contractible Reeb orbit, or the first Chern class of $ξ$ vanishes on $π_2(M)$, and the index of every contractible Reeb orbit is at least $2$. We present conditions for a weakly convex contact form to admit a well-defined cylindrical contact homology. The key point is a cancellation mechanism for boundary degenerations involving index-2 Reeb orbits, based on a parity property of holomorphic planes. |
| title | Cylindrical contact homology for weakly convex contact forms in dimension three |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2603.29352 |