Pseudo-Anosov representatives of stable Hamiltonian structures
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11784_2025_Article_1238.pdf
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Author(s)
Zung, Jonathan
Date Issued
September 8, 2025
Journal
Journal of Fixed Point Theory and Applications
Publisher
Springer International Publishing
Citation
Zung, J. Pseudo-Anosov representatives of stable Hamiltonian structures. J. Fixed Point Theory Appl. 27, 87 (2025).
Version
Final published version
Abstract
A pseudo-Anosov homeomorphism of a surface is a canonical representative of its mapping class. Conditional on the foundations of symplectic field theory, 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 ≥ 6 , p ≠ 0 , ± 1 , ± 2 mod q . The proof of the main theorem generalizes an argument of Barthelmé–Bowden–Mann.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s11784-025-01238-8
