Dynamics of iwip automorphisms of free products

TL;DR

This paper investigates the dynamics of iwip automorphisms in free products, providing criteria for free subgroup existence and analyzing centralizers and stabilizers within the outer automorphism group.

Contribution

It introduces a lamination-based criterion for free subgroup presence in subgroups of Out(G) and studies properties of iwip elements' centralizers and stabilizers.

Findings

Criteria for subgroups of Out(G) to contain free subgroups.

Analysis of centralizers of iwip automorphisms.

Description of stabilizers of associated laminations.

Abstract

Let $G$ be a free product and $\mathrm{Out}(G)$ the outer automorphism group of $G$. In this article using the theory of laminations we give a criterion for a subgroup $H$ of $\mathrm{Out}(G)$ to contain a nonabelian free subgroup. We also study the centraliser of an iwip element of $\mathrm{Out}(G)$ and the stabiliser of its associated lamination.