Obstructing Anosov flows on cusped 3-manifolds

Using results relating taut foliations, Heegaard–Floer homology and pseudo-Anosov flows, we find cusped hyperbolic 3-manifolds which are not the non-singular part of a pseudo-Anosov flow. In particular, we find the first examples of cusped hyperbolic 3-manifolds not admitting veering triangulations, confirming a conjecture of S. Schleimer.