Agol recently introduced the concept of a veering taut triangulation of a 3-manifold, which is a taut ideal triangulation with some extra combinatorial structure. Hodgson, Rubinstein, Tillmann and I show that each veering triangulation admits a strict angle structure, which is a necessary condition for the triangulation to be geometric. Computational evidence suggests that veering triangulations are very special, but that many manifolds have them.
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