ON THE MINIMUM OF ASYMPTOTIC TRANSLATION LENGTHS OF POINT-PUSHING PSEUDO-ANOSOV MAPS

摘要

Let S be a closed Riemann surface of genus p > 1 with one point x removed. Let F be the set of mapping classes on S isotopic to the identity on S U {x}. In this paper, we show that for any genus p> 1, the minimum L_c(F) of asymptotic translation lengths of all pseudo-Anosov elements of F satisfies the inequality 2/3 ≤ Lc(F) ≤ 1.