Fried's surgery conjecture for suspension pseudo-Anosov flows

Let Φ1\Phi_1 and Φ2\Phi_2 be suspension pseudo-Anosov flows. A Dehn-Goodman-Fried surgery is a surgery performed on a periodic orbit of a pseudo-Anosov flow to produce another pseudo-Anosov flow. Fried's surgery conjecture. Given any two suspension pseudo-Anosov flows Φ1\Phi_1 and Φ2\Phi_2, one can obtain Φ2\Phi_2 from Φ1\Phi_1 by performing a finite number of Dehn-Goodman-Fried surgeries. This would give an analogue, for comparing suspension flows, of the classification supplied by Fried's surgery theorem; the broader question of whether every non-transitive pseudo-Anosov flow can be obtained from a suspension flow by finitely many such surgeries is also stated as open in the surrounding discussion.

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Primary source

Ioannis Iakovoglou, “Markovian families for pseudo-Anosov flows”, arXiv:2509.19530 (2025).

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