Examples of Anosov flows with genus one Birkhoff sections

Chi Cheuk Tsang

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arXiv · 2402.00229

Examples of Anosov flows with genus one Birkhoff sections

Chi Cheuk Tsang

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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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Chi Cheuk Tsang. 2024-01-31. Examples of Anosov flows with genus one Birkhoff sections. https://arxiv.org/abs/2402.00229

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