an:01013771
Zbl 0884.57002
Bestvina, M.; Feighn, M.; Handel, M.
Laminations, trees, and irreducible automorphisms of free groups
EN
Geom. Funct. Anal. 7, No. 2, 215-244 (1997); erratum 7, No. 6, 1143 (1997).
00040265
1997
j
57M07 20F28 20E36 20E05
lamination; tree; outer automorphism; free group; word hyperbolicity
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 \(\varphi\).
S.C.Althoen (Flint)