%0 Journal Article
%T The Recognition Theorem for Out(F_n)
%A Mark Feighn
%A Michael Handel
%J Mathematics
%D 2006
%I arXiv
%X 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 $\phi\in\Out(F_n)$, $\phi^{K_n}$ is forward rotationless. An important part of our analysis is to show that rotationless elements are represented by particularly nice relative train track maps.
%U http://arxiv.org/abs/math/0612702v2