Fried's surgery conjecture for suspension pseudo-Anosov flows
Fried's surgery conjecture for suspension pseudo-Anosov flows
Let and 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 and , one can obtain from 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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