Groups acting on veering pairs and Kleinian groups

Abstract We show that some subgroups of the orientation‐preserving circle homeomorphism group with invariant veering pairs of laminations are hyperbolic 3‐orbifold groups. On the way, we show that from a veering pair of laminations, one can construct a loom space (in the sense of Schleimer–Segerman) as a quotient. Our approach does not assume the existence of any 3‐manifold to begin with, so this is a geometrization‐type result, and supersedes some of the results regarding the relation among veering triangulations, pseudo‐Anosov flows, taut foliations in the literature.