When loxodromics are pseudo-Anosovs on witnesses

Abstract

In this paper, we prove that for subgroups acting on admissible multiarc and curve graphs and for the handlebody group acting on the disk graph, the loxodromic elements are exactly those for which some pure power is a pseudo-Anosov on a witness. This generalizes the result of Masur and Minsky that the elements of the mapping class group that act loxodromically on the curve graph are the pseudo-Anosov elements.