Stable loops and almost transverse surfaces

Abstract

We use veering triangulations to study homology classes on the boundary of the cone over a fibered face of a compact fibered hyperbolic three-manifold. This allows us to give a handson proof of an extension of Mosher’s transverse surface theorem to the setting of manifolds with boundary. We also show that the cone over a fibered face is dual to the cone generated by the homology classes of a canonical finite collection of curves called minimal stable loops living in the associated veering triangulation.