Taut branched surfaces from veering triangulations

Abstract

Let $M$ be a closed hyperbolic $3$–manifold with a fibered face $\sigma$ of the unit ball of the Thurston norm on $H_2\left(M\right)$. If $M$ satisfies a certain condition related to Agol’s veering triangulations, we construct a taut branched surface in $M$ spanning $\sigma$. This partially answers a 1986 question of Oertel, and extends an earlier partial answer due to Mosher.