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

Abstract

We give a short proof of a theorem of Handel and Mosher stating that any finitely generated subgroup of $\text{Out}(F_N)$ 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 $\text{Out}(F_N)$.

10 pages

References in corpus (2)

• Reducing systems for very small trees
• Subgroup classification in Out(F_n)

Cited by in corpus (2)

• The Tits alternative for the automorphism group of a free product
• Ergodic decompositions for folding and unfolding paths in Outer space