Veering triangulations and the Thurston norm: homology to isotopy

Abstract

We show that a veering triangulation $\tau$ specifies a face $\sigma$ of the Thurston norm ball of a closed three-manifold, and computes the Thurston norm in the cone over $\sigma$. Further, we show that $\tau$ collates exactly the taut surfaces representing classes in the cone over $\sigma$ up to isotopy. The analysis includes nonlayered veering triangulations and nonfibered faces.