The veering ancestry graph and a conjecture of Ghys

A conjecture of Ghys asserts that any two transitive Anosov flows with orientable invariant foliations are almost orbit equivalent. In this talk, I will outline a connection between pseudo-Anosov flows and veering triangulations, and use it to reformulate Ghys’ conjecture in terms of properties of the veering ancestry graph. I will then discuss an algorithm whose implementation can be used to construct large subgraphs of this graph, and conclude by presenting the experimental data obtained.
This is joint work with Henry Segerman.