Loxodromic elements for the relative free factor complex

Abstract

In this paper we prove that a fully irreducible outer automorphism relative to a non-exceptional free factor system acts loxodromically on the relative free factor complex as defined by Handel and Mosher. We also prove a north-south dynamic result for the action of such outer automorphisms on the closure of relative outer space.

arXiv comment27 pages, 11 figures, incorporating referees suggestions. To appear in Geometriae Dedicata