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

O. Bogopolski·A. Martino·E. Ventura
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Abstract

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 $GL_2(\mathbb{Z})$.

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O. Bogopolski, A. Martino, E. Ventura. 2006-02-15. The automorphism group of a free-by-cyclic groups in rank 2. https://arxiv.org/abs/math/0602327

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