### Subgroups of Out(F_n)

#### Michael Handel, CUNY Lehman

Abstract: Two topics to be discussed are:

1) (joint work with Mark Feighn) An explicit description of all maximal rank abelian subgroups of Out(F_n).

2) Theorem (joint work with Lee Mosher) : If H is a subgroup of Out(F_n) then either H contains a completely irreducible element or there is a finite index subgroup H' of H and an H'-invariant proper free factor system.

This theorem is the analog of a theorem of Ivanov that states that if H is a subgroup of the mapping class group then either H contains a pseudo-Anosov element or there is a finite index subgroup H' of H and an H'-invariant curve system.