Groups, Geometry, and Dynamics


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Volume 5, Issue 1, 2011, pp. 39–106
DOI: 10.4171/GGD/116

Published online: 2011-01-19

The Recognition Theorem for Out(Fn)

Mark Feighn[1] and Michael Handel[2]

(1) Rutgers University, Newark, USA
(2) Lehman College, CUNY, Bronx, USA

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

Keywords: Outer automorphisms, free group

Feighn Mark, Handel Michael: The Recognition Theorem for Out(Fn). Groups Geom. Dyn. 5 (2011), 39-106. doi: 10.4171/GGD/116