Stabilizers of R-trees with Free Isometric Actions
نویسنده
چکیده
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+(φ) is the forward limit tree of an atoroidal iwip element φ ∈ Out(FN ) 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(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.
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