Title: Cusp geometry of fibered 3-manifolds
Abstract: Let be a surface with punctures, and suppose that is a pseudo-Anosov homeomorphism fixing a puncture of . Then the mapping torus of is a hyperbolic 3-manifold , which contains a maximal cusp corresponding to the puncture . We show that the geometry of the maximal cusp can be predicted, up to explicit multiplicative error, by the action of on the complex of essential arcs of in the surface , denoted .
This result is motivated by an analogous theorem of Brock, which predicts the volume of in terms of the action of on the pants graph . However, in contrast with Brock’s theorem. our result gives effective estimates, and is proved using completely elementary methods. This is joint work with Saul Schleimer.