The Recognition Theorem for

  • Mark Feighn

    Rutgers University, Newark, USA
  • Michael Handel

    Lehman College, CUNY, Bronx, USA


Our goal is to find dynamic invariants that completely determine elements of the outer automorphism group of the free group of rank . To avoid finite order phenomena, we do this for forward rotationless elements. This is not a serious restriction. For example, there is depending only on such that, for all , is forward rotationless. An important part of our analysis is to show that rotationless elements are represented by particularly nice relative train track maps.

Cite this article

Mark Feighn, Michael Handel, The Recognition Theorem for . Groups Geom. Dyn. 5 (2011), no. 1, pp. 39–106

DOI 10.4171/GGD/116