Let $\phi$ be an automorphism of a free group $F_n$ of rank $n$, and let $M_{ \phi}=F_n \rtimes_{ \phi} \mathbb{ Z}$ be the corresponding mapping torus of $\phi$. We study the group $Out(M_{ \phi})$ under certain technical conditions on $\phi$. 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 $\phi$ in $GL_2(\mathbb{ Z})$.
Categories: math.GR