Loxodromic elements for the relative free factor complex

TL;DR

This paper proves that certain automorphisms act loxodromically on the relative free factor complex and exhibit north-south dynamics on the closure of relative outer space, advancing understanding of their geometric actions.

Contribution

It establishes loxodromic action and dynamic properties of fully irreducible outer automorphisms relative to free factor systems.

Findings

Proves loxodromic action on the relative free factor complex.

Demonstrates north-south dynamics on the closure of relative outer space.

Extends understanding of automorphism actions in geometric group theory.

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.