The Recognition Theorem for Out(F_n)

Details The Recognition Theorem for Out(F_n) The Recognition Theorem for Out(F_n)

2006-12-22

arxiv.org/abs/math/0612702v2

Mathematics

Group Theory

68 pages

Scientific paper

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.

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