Abstract: In the 1990s, Gabai and Mosher proved a dramatic existence theorem concerning pseudo-Anosov flows transverse to taut, finite-depth foliations of 3-manifolds. Unfortunately, the proof is still unwritten. We recently proved the first half of a refinement of the Gabai-Mosher theorem using ideas from the theory of veering triangulations, and the second half is work in progress. One motivation for this project is to take a first step toward a proof of Mosher's “Norm and Flow Finiteness Conjecture,” which claims that the Thurston norm for a compact hyperbolic 3-manifold is determined by finitely many pseudo-Anosov flows. (Joint work with Chi Cheuk Tsang).
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