Dehn twists combined with pseudo-Anosov maps

Abstract

Let S be a Riemann surface of type (p, n) with 3p + n > 4 and n ≥ 1. Let a be a puncture of S. We show that for any Dehn twist t_c along a simple closed geodesic c on S, there exists a sequence {f_m} of pseudo-Anosov maps of S such that for sufficiently large integers m, the products f_m $\circ$ t_c^k are pseudo-Anosov for all integers k. As a corollary, we prove that for a multi-twist M₂ on $\tilde{S}$ along two disjoint simple closed geodesics, there are infinitely many pseudo-Anosov maps of S that are isotopic to M₂ as a is filled in.