Pseudo-Anosov Reeb flows and contact structures
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908746275356672 |
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| author | Chaidez, Julian Pan, Yijie |
| author_facet | Chaidez, Julian Pan, Yijie |
| contents | We introduce the notion of a pseudo-Anosov contact structure, which admits a type of singular contact form with pseudo-Anosov Reeb flow. We prove that contact homology detects the free homotopy classes of closed orbits of any pseudo-Anosov Reeb flow and that any pseudo-Anosov contact structure is universally tight and torsion free. Many applications are given, including new cases of the Finiteness Conjecture for transitive pseudo-Anosov flows. Our proofs use a flavor of contact homology graded by a free homotopy class of loops, defined for any contact manifold. We establish several properties of this type of contact homology that may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12698 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pseudo-Anosov Reeb flows and contact structures Chaidez, Julian Pan, Yijie Symplectic Geometry Dynamical Systems Geometric Topology 53D10, 53D42, 37D20, 37D40 We introduce the notion of a pseudo-Anosov contact structure, which admits a type of singular contact form with pseudo-Anosov Reeb flow. We prove that contact homology detects the free homotopy classes of closed orbits of any pseudo-Anosov Reeb flow and that any pseudo-Anosov contact structure is universally tight and torsion free. Many applications are given, including new cases of the Finiteness Conjecture for transitive pseudo-Anosov flows. Our proofs use a flavor of contact homology graded by a free homotopy class of loops, defined for any contact manifold. We establish several properties of this type of contact homology that may be of independent interest. |
| title | Pseudo-Anosov Reeb flows and contact structures |
| topic | Symplectic Geometry Dynamical Systems Geometric Topology 53D10, 53D42, 37D20, 37D40 |
| url | https://arxiv.org/abs/2512.12698 |