Lipschitz retraction and distortion for subgroups of Out(Fn)

Michael Handel, Lee Mosher

Research output: Contribution to journalArticle

6 Scopus citations


Given a free factor A of the rank n free group Fn, we characterize when the subgroup of Out(Fn) that stabilizes the conjugacy class of A is distorted in Out(Fn). We also prove that the image of the natural embedding of Aut(Fn-1) in Aut(Fn) is nondistorted, that the stabilizer in Out(Fn) of the conjugacy class of any free splitting of Fn is nondistorted and we characterize when the stabilizer of the conjugacy class of an arbitrary free factor system of Fn 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(Fn) and Aut(Fn).

Original languageEnglish (US)
Pages (from-to)1535-1579
Number of pages45
JournalGeometry and Topology
Issue number3
StatePublished - Jun 15 2013

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


  • Distortion
  • Lipschitz retraction
  • Subgroups of Out(F-n)

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