Subgroup classification in Out(Fn)

Lee Mosher, Rutgers University, Newark

For any subgroup H of Out(Fn), either H has a finite index subgroup that fixes the conjugacy class of some proper, nontrivial free factor of Fn, or H contains a fully irreducible element phi, meaning that no positive power of phi fixes the conjugacy class of any proper, nontrivial free factor of Fn.