Geometric & Functional Analysis GAFA

, Volume 7, Issue 2, pp 215-244

First online:

Laminations, trees, and irreducible automorphisms of free groups

  • M. BestvinaAffiliated withMladen Bestvina, Dept. of Math., University of Utah, Salt Lake City, UT 84112, USA e-mail:
  • , M. FeighnAffiliated withMark Feighn, Dept. of Math., Rutgers University, Newark, NJ 07102, USA e-mail:
  • , M. HandelAffiliated withMichael Handel, Dept. of Math., CUNY, Lehman College, Bronx, NY 10468, USA e-mail:

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We examine the action of Out(F n ) on the set of (irreducible) laminations. Consequences include a special case of the Tits alternative for Out(F n ), the discreteness of certain naturally arising group actions on trees, and word hyperbolicity of certain semidirect products.