TOPOLOGICAL ENTROPY OF PSEUDO-ANOSOV MAPS ON PUNCTURED SURFACES VS. HOMOLOGY OF MAPPING TORI

Abstract

We investigate the relation between the topological entropy of pseudo-Anosov maps on surfaces with punctures and the rank of the first homology of their mapping tori. On the surface S of genus g with n punctures, we show that the minimal entropy of a pseudo-Anosov map is bounded from above by (k + 1) log(k + 3)/|chi(S)| up to a constant multiple when the rank of the first homology of the mapping torus is k + 1 and k, g, n satisfy a certain assumption. This is a partial generalization of precedent works of Tsai and AgolLeininger-Margalit.