Relative Currents

TL;DR

This paper introduces the concept of currents relative to free factor systems and demonstrates that certain automorphisms exhibit uniform north-south dynamics on a related space.

Contribution

It defines relative currents and proves dynamic behavior of fully irreducible automorphisms in this new context.

Findings

Fully irreducible automorphisms act with north-south dynamics

Introduction of currents relative to free factor systems

Establishment of uniform dynamics on a subspace

Abstract

In this paper we define currents relative to a free factor system. We prove that a fully irreducible outer automorphism relative to a free factor system acts with uniform north-south dynamics on a subspace of the space of projective relative currents.