The recognition theorem for Out (Fn)

Mark Feighn, Michael Handel

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


Our goal is to find dynamic invariants that completely determine elements of the outer automorphism group Out.Fn) 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 Kn > 0 depending only on n such that, for all φ ε Out.Fn), φKn is forward rotationless. An important part of our analysis is to show that rotationless elements are represented by particularly nice relative train track maps.

Original languageEnglish (US)
Pages (from-to)39-106
Number of pages68
JournalGroups, Geometry, and Dynamics
Issue number1
StatePublished - 2011

All Science Journal Classification (ASJC) codes

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


  • Free group
  • Outer automorphisms


Dive into the research topics of 'The recognition theorem for Out (Fn)'. Together they form a unique fingerprint.

Cite this