Abstract: In this talk we will analyze fibers of 3-manifolds that fiber over S1. We will show that if the genus of the fiber is at least 38t (where t is the number of tetrahedra required to construct the manifold) then the fiber is strongly cylindrical (the term will be defined in the talk). In particular, this implies that the translation distance induced by the monodromy on the curve complex of the fiber is at most 1.
The talk is based on joint work with Kazuhiro Ichihara (Nihon University) and Tsuyoshi Kobayashi (Nara Women's University).