When is a polynomially growing automorphism of $F_n$ geometric ?

Abstract

The main result of this paper is an algorithmic answer to the question raised in the title, up to replacing the given $\hat{\varphi }\in Out(F_n)$ by a positive power. In order to provide this algorithm, it is shown that every polynomially growing automorphism $\hat{\varphi }$ can be represented by an iterated Dehn twist on some graph-of-groups $\mathcal{G}$ with ${\pi }_1\mathcal{G}=F_n$. One then uses results of two previous papers \cite{KY01, KY02} as well as some classical results such as the Whitehead algorithm to prove the claim.

References in corpus (1)

• Partial Dehn twists of free groups relative to local Dehn twists - a dichotomy