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arXiv · 2611.00977

There is only one transitive Anosov flow (in dimension 3, with orientable foliations, up to bicontact padding and Goodman surgeries)

Thomas Barthelmé·Federico Salmoiraghi·Chi Cheuk Tsang
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Abstract

We introduce a new surgical operation on Anosov flows, which we call bicontact padding surgery. The operation is defined using the machinery of strongly adapted bicontact structures, and involves inserting a 'padding' layer where one of the contact structures rotates many times around the Reeb flow of the other. We show that every skew Anosov flow with orientable stable and unstable foliations can be transformed into a finite cover of a geodesic flow using bicontact padding surgery and Goodman surgery. Together with previous results, this implies that every transitive Anosov flow with orientable stable and unstable foliations can be transformed into a suspension flow using bicontact padding surgery and Goodman surgery. This gives some progress towards the Christy-Fried-Ghys conjecture, which predicts that the same statement is true using only Goodman surgery.

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Thomas Barthelmé, Federico Salmoiraghi, Chi Cheuk Tsang. 2026-10-31. There is only one transitive Anosov flow (in dimension 3, with orientable foliations, up to bicontact padding and Goodman surgeries). https://arxiv.org/abs/2611.00977

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