Stabilizers of R-trees with free isometric actions of FN

We prove that if T is an R-tree with a minimal free isometric action of F-N, then the Out(F-N)-stabilizer of the projective class [T] is virtually cyclic. For the special case where T = T+(phi) is the forward limit tree of an atoroidal iwip element phi epsilon Out(F-N) this is a consequence of the results of Bestvina, Feighn and Handel [6], via very different methods. We also derive a new proof of the Tits alternative for subgroups of Out(F-N) containing an iwip (not necessarily atoroidal): we prove that every such subgroup G <= Out(F-N) is either virtually cyclic or contains a free subgroup of rank two. The general case of the Tits alternative for subgroups of Out(F-N) is due to Bestvina, Feighn and Handel.