An upper bound on the asymptotic translation length on the curve complex

Chenxi Wu (Rutgers)

Abstract: A pseudo-Anosov map induces a map from the curve graph to itself, and a basic question is to study the asymptotic translation length which is known to be a non-zero rational number. I will give an introduction on prior works on the study of this asymptotic translation length, and present an improved upper bound for the asymptotic translation length for pseudo-Anosov maps inside a fibered cone, which generalizes the previous result on sequences with small translation length on curve graphs by Kin and Shin. This is a joint work by Hyungryul Baik and Hyunshik Shik.