Michael Handel, Lee Mosher
Published 2010-09-25, updated 2012-05-25Version 3
Given a free factor A of the rank n free group F_n, we characterize when the subgroup of Out(F_n) that stabilizes the conjugacy class of A is distorted in Out(F_n). We also prove that the image of the natural embedding of Aut(F_{n-1}) in Aut(F_n) is nondistorted, that the stabilizer in Out(F_n) of the conjugacy class of any free splitting of F_n is nondistorted, and we characterize when the stabilizer of the conjugacy class of an arbitrary free factor system of F_n is distorted. In all proofs of nondistortion, we prove the stronger statement that the subgroup in question is a Lipschitz retract. As applications we determine Dehn functions and automaticity for Out(F_n) and Aut(F_n).
Comments: Version 3: 35 pages. Revised for publication. Changes from previous versions: significant economies in exposition. Added an explicit description of the stabilizer of a free splitting, in Lemma 18
Distortion in Free Nilpotent Groups
Limits of conjugacy classes under iterates of Hyperbolic elements of $\mathsf{Out(\mathbb{F})}$
Distortion of surfaces in $3$--manifolds
![QR code for arXiv:1009.5018 [math.GR]](http://oss.arxitics.com/images/favicon.svg)