The canonical decomposition of once-punctured torus bundles

In this paper, we determine the canonical polyhedral decomposition of every
hyperbolic once-punctured torus bundle over the circle. In fact, we show that
the only ideal polyhedral decomposition that is straight in the hyperbolic
structure and that is invariant under a certain involution is the ideal
triangulation defined by Floyd and Hatcher. Unlike previous work on this
problem, the techniques we use are not geometric. Instead, they involve angled
polyhedral decompositions, thin position and a version of almost normal surface
theory.