A short proof of Handel and Mosher's alternative for subgroups of Out$(F_N)$

Camille Horbez

doi:10.4171/ggd/361

JournalsggdVol. 10, No. 2pp. 709–721

A short proof of Handel and Mosher's alternative for subgroups of Out $(F_{N})$

Camille Horbez
Université Paris-Sud, Orsay, France

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Abstract

We give a short proof of a theorem of Handel and Mosher [21] stating that any finitely generated subgroup of Out $(F_{N})$ either contains a fully irreducible automorphism, or virtually fixes the conjugacy class of a proper free factor of $F_{N}$ , and we extend their result to non finitely generated subgroups of Out $(F_{N})$ .

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Camille Horbez, A short proof of Handel and Mosher's alternative for subgroups of Out $(F_{N})$ . Groups Geom. Dyn. 10 (2016), no. 2, pp. 709–721

DOI 10.4171/GGD/361