The automorphism group of a free-by-cyclic groups in rank 2

Bogopolski, O.; Martino, A.; Ventura, E.

The automorphism group of a free-by-cyclic groups in rank 2

Authors

Bogopolski, O.

Martino, A.

Ventura, E.

Description

Let $ϕ$ be an automorphism of a free group $F_n$ of rank $n$, and let $M_ϕ=F_n \rtimes_ϕ \mathbb{Z}$ be the corresponding mapping torus of $ϕ$. We study the group $Out(M_ϕ)$ under certain technical conditions on $ϕ$. Moreover, in the case of rank 2, we classify the cases when this group is finite or virtually cyclic, depending on the conjugacy class of the image of $ϕ$ in $GL_2(\mathbb{Z})$.
14 pages