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The Recognition Theorem for Out(F_n)

Mark Feighn·Michael Handel
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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 $ϕ\in\Out(F_n)$, $ϕ^{K_n}$ is forward rotationless. An important part of our analysis is to show that rotationless elements are represented by particularly nice relative train track maps.

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Mark Feighn, Michael Handel. 2009-02-15. The Recognition Theorem for Out(F_n). https://arxiv.org/abs/math/0612702

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