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

Horbez, Camille

doi:10.4171/GGD/361

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Groups, Geometry, and Dynamics

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Volume 10, Issue 2, 2016, pp. 709–721

DOI: 10.4171/GGD/361

Published online: 2016-06-09

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

Camille Horbez^[1]

(1) Université Paris-Sud, Orsay, France

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$(F_N)$.

Keywords: Out$(F_N)$, subgroup classification

Horbez Camille: A short proof of Handel and Mosher's alternative for subgroups of Out$(F_N)$. Groups Geom. Dyn. 10 (2016), 709-721. doi: 10.4171/GGD/361