ON UNIT STABLE LENGTHS OF TRANSLATIONS OF POINT-PUSHING PSEUDO-ANOSOV MAPS ON CURVE COMPLEXES
Let be a hyperbolic Riemann surface of genus with one puncture x. In this paper, we consider the subgroup of the mapping class group of that consists of point-pushing mapping classes, and show that the minimum of stable translation lengths for the actions of all pseudo-Anosov elements of on the curve complex is one. It is well known that every pseudo-Anosov element determines an oriented filling closed geodesic g on We further show that can be achieved by those pseudo-Anosov elements f so that g intersect some simple closed geodesics only once. As consequences, we prove that the set of the stable translation lengths for the actions of all pseudo-Anosov elements of is unbounded. We also give a sufficient condition for a pseudo-Anosov element to have invariant bi-infinite geodesics in
point-pushing, pseudo-Anosov, Dehn twists, curve complex, filling curves.