Laminations, trees, and irreducible automorphisms of free groups (Q1355448)

Suppose \(H\) is a subgroup of \(\text{Out} (F_n)\), the outer automorphism group of \(F_n\), the free group of rank \(n\), that contains an irreducible outer automorphism \(\varphi\) of infinite order. The authors show that either \(H\) contains \(F_2\) or \(H\) is virtually cyclic. They demonstrate the word hyperbolicity of semidirect products \(F_n\rtimes \mathbb{Z}\) induced by infinite order irreducible elements of \(\text{Out} (F_n)\) and generalize this to certain semidirect products \(F_n\rtimes F_2\). They also show that if \(A\) is a finitely generated subgroup of \(F_n\) of infinite index, then the action of \(A\) on \(T^+\) is discrete, where \(T^+\) is a \(\varphi\)-fixed real tree associated to \(\varphi\).