The automorphism group of a free-by-cyclic group in rank 2
نویسندگان
چکیده
Let φ be an automorphism of a free group Fn of rank n, and let Mφ = Fn oφ Z be the corresponding mapping torus of φ. We study the group Out(Mφ) 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 GL2(Z). As an application, we solve the isomorphism problem for the family of F2-by-Z groups, in terms of the two defining automorphisms.
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