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Article Dans Une Revue Journal of Group Theory Année : 2011

Stabilizers of ℝ-trees with free isometric actions of FN

Résumé

We prove that if $T$ is an $\mathbb R$-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 $\phi\in Out(F_N)$ this is a consequence of the results of Bestvina, Feighn and Handel, 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 $G\le Out(F_N)$ 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.

Dates et versions

hal-01318392 , version 1 (19-05-2016)

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Citer

Ilya Kapovich, Martin Lustig. Stabilizers of ℝ-trees with free isometric actions of FN. Journal of Group Theory, 2011, 14 (5), pp.673-694. ⟨10.1515/JGT.2010.070⟩. ⟨hal-01318392⟩
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