3/5/2009

Lee Mosher
Rutgers University, Newark

Subgroup classification in Out(F_n)

We prove that for every subgroup G of Out(F_n), one of two alternatives holds: either there is a finite index subgroup H < G and a nontrivial proper free factor A of F_n such that each element of H fixes the conjugacy class of A; or there is an element g \in G such that no nontrivial power of g fixes the conjugacy class of any nontrivial proper free factor of F_n. This theorem is an analogue of Ivanov's classification of subgroups of surface mapping class groups. It has application to bounded 2nd cohomology of Out(F_n), by combining with results of Bestvina-Feighn and of Hamenstadt. This work is joint with Michael Handel.