Commensurations of Out(F n )
Publications Mathématiques de l'IHÉS, Tome 105 (2007), pp. 1-48.

Let Out(F n ) denote the outer automorphism group of the free group F n with n>3. We prove that for any finite index subgroup Γ<Out(F n ), the group Aut(Γ) is isomorphic to the normalizer of Γ in Out(F n ). We prove that Γ is co-Hopfian: every injective homomorphism Γ→Γ is surjective. Finally, we prove that the abstract commensurator Comm(Out(F n )) is isomorphic to Out(F n ).

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     author = {Farb, Benson and Handel, Michael},
     title = {Commensurations of {Out}$(F_n)$},
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Farb, Benson; Handel, Michael. Commensurations of Out$(F_n)$. Publications Mathématiques de l'IHÉS, Tome 105 (2007), pp. 1-48. doi : 10.1007/s10240-007-0007-7. http://www.numdam.org/articles/10.1007/s10240-007-0007-7/

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