Harry Hyungryul Baik - Normal generators for mapping class groups are abundant in the fibered cone

We show that for almost all primitive integral cohomology classes in the fibered cone of a closed fibered hyperbolic 3-manifold, the monodromy normally generates the mapping class group of the fiber. The key idea of the proof is to use Fried’s theory of suspension flow and dynamic blow-up of Mosher. If the time permits, we also discuss the non-existence of the analog of Fried’s continuous extension of the normalized entropy over the fibered face in the case of asymptotic translation lengths on the curve complex. Joint work with Eiko Kin, Hyunshik Shin and Chenxi Wu.