On the conjugacy problem for automorphisms of free groups. With an addendum (Q1918445)

The author considers the conjugacy problem for outer automorphisms of a free group. If \(\Phi\) is an outer automorphism of the free group \(F_n\) of rank \(n\), then \(\Phi\) is called reducible if there are proper free factors \(F_1,\dots,F_k\) of \(F_n\) such that \(\Phi\) transitively permutes the conjugacy classes of the \(F_i\)'s and \(F_1*F_2*\dots*F_k\) is a free factor of \(F_n\). If \(\Phi\) is not reducible, then it is called irreducible. The author proves that for irreducible outer automorphisms of \(F_n\), the conjugacy problem has a solution and comments that the general problem is still open. The method of proof uses the Bestvina-Handel train tracks and actually proves that \(\Phi_1\) and \(\Phi_2\) are conjugate if they have the same set of train track representatives. In the addendum he clarifies the proof by replacing the key lemma of the paper by giving a new formulation and a more explicit proof.