We prove that if T is an ℝ-tree with a minimal free isometric action of FN, then the Out(FN)-stabilizer of the projective class T is virtually cyclic. For the special case where T T(φφ) is the forward limit tree of an atoroidal iwip element φφ ∈ Out(FN) this is a consequence of the results of Bestvina, Feighn and Handel Geom. Funct. Anal. 7: 215244, 1997, via very different methods. We also derive a new proof of the Tits alternative for subgroups of Out(FN) containing an iwip (not necessarily atoroidal): we prove that every such subgroup G ≤ Out(FN) is either virtually cyclic or contains a free subgroup of rank two. The general case of the Tits alternative for subgroups of Out(FN) is due to Bestvina, Feighn and Handel.
ASJC Scopus subject areas
- Algebra and Number Theory