The Recognition Theorem for Out(F_n)

Abstract

Our goal is to find dynamic invariants that completely determine elements of the outer automorphism group $\Out(F_n)$ of the free group $F_n$ of rank $n$. To avoid finite order phenomena, we do this for {\it forward rotationless} elements. This is not a serious restriction. For example, there is $K_n>0$ depending only on $n$ such that, for all $ϕ\in\Out(F_n)$, ${\varphi }^{K_n}$ is forward rotationless. An important part of our analysis is to show that rotationless elements are represented by particularly nice relative train track maps.

68 pages

References in corpus (1)

• Free-group automorphisms, train tracks and the beaded decomposition

Cited by in corpus (2)

• Subgroup classification in Out(F_n)
• The mapping-torus of a free group automorphism is hyperbolic relative to the canonical subgroups of polynomial growth