Commensurations of Out$(F_n)$

Farb, Benson; Handel, Michael

doi:10.1007/s10240-007-0007-7

Geodesic

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Commensurations of Out

(F_{n})

Farb, Benson ; Handel, Michael

Publications Mathématiques de l'IHÉS, Tome 105 (2007), pp. 1-48

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Résumé

Let $O u t (F_{n})$ denote the outer automorphism group of the free group $F_{n}$ with $n > 3$ . We prove that for any finite index subgroup $Γ < O u t (F_{n})$ , the group $A u t (Γ)$ is isomorphic to the normalizer of $Γ$ in $O u t (F_{n})$ . We prove that $Γ$ is co-Hopfian: every injective homomorphism $Γ \to Γ$ is surjective. Finally, we prove that the abstract commensurator $C o m m (O u t (F_{n}))$ is isomorphic to $O u t (F_{n})$ .

DOI : 10.1007/s10240-007-0007-7

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     author = {Farb, Benson and Handel, Michael},
     title = {Commensurations of {Out}$(F_n)$},
     journal = {Publications Math\'ematiques de l'IH\'ES},
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     publisher = {Springer},
     volume = {105},
     year = {2007},
     doi = {10.1007/s10240-007-0007-7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-007-0007-7/}
}

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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

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