Examples of Anosov flows with genus one Birkhoff sections

2024/01/31 by Tsang, Chi Cheuk
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2402.00229

Abstract

We show that a transitive Anosov flow with orientable stable and unstable foliations that either (i) admits a Birkhoff section whose first return map is a Penner type pseudo-Anosov map, or (ii) is totally periodic admits a genus one Birkhoff section. This provides evidence for a conjecture of Fried and Ghys. The proof utilizes a result of the author on the horizontal Goodman surgery operation. To apply this result for showing (i), we establish correspondence between horizontal Goodman surgery on pseudo-Anosov flows and horizontal surgery on veering triangulations in the layered setting.

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• Oriented Birkhoff sections of Anosov flows
• Pseudo-Anosov representatives of stable Hamiltonian structures
• Horizontal Goodman surgery and almost equivalence of pseudo-Anosov flows
• Goodman surgery and projectively Anosov flows