POINT-PUSHING PSEUDO-ANOSOV MAPPING CLASSES AND THEIR ACTIONS ON THE CURVE COMPLEX
Let S be an analytically finite Riemann surface of type with which is equipped with a hyperbolic metric and contains at least one puncture x. Let be the curve complex endowed with a path metric It is known that a point-pushing pseudo-Anosov mapping class f on S determines a filling closed geodesic c on and that every non-preperipheral vertex u in determines a simple curve on In this paper, we consider the action of f on We describe all geodesic segments in that connect u and when We also give sufficient conditions with respect to the intersection points between c and for the path distance to be larger.
Riemann surfaces, pseudo-Anosov, Dehn twists, curve complex, filling curves.