2024/10/03 by Jonathan Zung, Zung, Jonathan
Engineering · Physics and Astronomy · #Control and Stability of Dynamical Systems #FOS: Mathematics #Geometric Topology (math.GT) #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2410.02186
openalex publication_date 2024/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 S3 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.