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

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

2006-02-15

arxiv.org/abs/math/0602327v1

Mathematics

Group Theory

14 pages

Scientific paper

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 $GL_2(\mathbb{Z})$.

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