Pseudo-Anosov representatives of stable Hamiltonian structures
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910630791872512 |
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| author | Zung, Jonathan |
| author_facet | Zung, Jonathan |
| contents | A pseudo-Anosov homeomorphism of a surface is a canonical representative of its mapping class. In this paper, we explain that a transitive pseudo-Anosov flow is similarly a canonical representative of its stable Hamiltonian class. It follows that there are finitely many pseudo-Anosov flows admitting positive Birkhoff sections on any given rational homology 3-sphere. This result has a purely topological consequence: any 3-manifold can be obtained in at most finitely many ways as $p/q$ surgery on a fibered hyperbolic knot in $S^3$ for a slope $p/q$ satisfying $q\geq 6$, $p\neq 0, \pm 1, \pm 2 \mod q$. The proof of the main theorem generalizes an argument of Barthelmé--Bowden--Mann. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02186 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pseudo-Anosov representatives of stable Hamiltonian structures Zung, Jonathan Geometric Topology Symplectic Geometry A pseudo-Anosov homeomorphism of a surface is a canonical representative of its mapping class. In this paper, we explain that a transitive pseudo-Anosov flow is similarly a canonical representative of its stable Hamiltonian class. It follows that there are finitely many pseudo-Anosov flows admitting positive Birkhoff sections on any given rational homology 3-sphere. This result has a purely topological consequence: any 3-manifold can be obtained in at most finitely many ways as $p/q$ surgery on a fibered hyperbolic knot in $S^3$ for a slope $p/q$ satisfying $q\geq 6$, $p\neq 0, \pm 1, \pm 2 \mod q$. The proof of the main theorem generalizes an argument of Barthelmé--Bowden--Mann. |
| title | Pseudo-Anosov representatives of stable Hamiltonian structures |
| topic | Geometric Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2410.02186 |