Georgia Institute of Technology College of Sciences

Let M be a closed hyperbolic 3-manifold with a fibered face \sigma of the unit ball of the Thurston norm on H_2(M). 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. I will not assume knowledge of the Thurston norm, branched surfaces, or veering triangulations.