The Recognition Theorem for Out(<var>F</var><sub><var>n</var></sub>)

  • 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 Out(Fn)\mathrm{Out}(F_n) of the free group FnF_n of rank nn. To avoid finite order phenomena, we do this for forward rotationless elements. This is not a serious restriction. For example, there is Kn>0K_n>0 depending only on nn such that, for all ϕOut(Fn)\phi\in\mathrm{Out}(F_n), ϕKn\phi^{K_n} 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 Out(<var>F</var><sub><var>n</var></sub>). Groups Geom. Dyn. 5 (2011), no. 1, pp. 39–106

DOI 10.4171/GGD/116