Generalized north-south dynamics on the space of geodesic currents

Abstract

We prove uniform north-south dynamics type results for the action of $\phi \in Out(F_N)$ on the space of projectivized geodesic currents $\mathbb{P}Curr(S)=\mathbb{P}Curr(F_N)$, where $\phi$ is induced by a pseudo-Anosov homeomorphism on a compact surface S with boundary such that ${\pi }_1(S)=F_N$. As an application, we show that for a subgroup $H\le Out(F_N)$, containing an iwip, either $H$ contains a hyperbolic iwip or $H$ is contained in the image in $Out(F_N)$ of the mapping class group of a surface with a single boundary component.

20 pages, 2 figures, v3: Minor corrections

References in corpus (4)

• Subgroup classification in Out(F_n)
• A hyperbolic Out(F_n)-complex
• Dynamics of hyperbolic iwips
• The actions of $Out(F_k)$ on the boundary of Outer space and on the space of currents: minimal sets and equivariant incompatibility

Cited by in corpus (8)

• The Poisson boundary of $\text{Out}(F_N)$
• Boundaries of relative factor graphs and subgroup classification for automorphisms of free products
• Counting loxodromics for hyperbolic actions
• North-South dynamics of hyperbolic free group automorphisms on the space of currents
• Dynamics of hyperbolic iwips
• Hyperbolic extensions of free groups from atoroidal ping-pong
• Atoroidal dynamics of subgroups of Out(F_N)
• Currents relative to a malnormal subgroup system