On the conjugacy problem for automorphisms of free groups. With an addendum
type: Item
instance of: scholarly article
title: On the conjugacy problem for automorphisms of free groups. With an addendum
zbMATH Open document ID: 0858.20022
DOI: 10.1016/0040-9383(95)00035-6
author: Jérôme Los
published in: Topology
publication date: 1997-03-16T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 20E05
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 912201
zbMATH Keywords: conjugacy problem
zbMATH Keywords: outer automorphisms
zbMATH Keywords: free factors
zbMATH Keywords: irreducible outer automorphisms
zbMATH Keywords: train tracks
MaRDI profile type: Publication
full work available at URL: 0040-9383(95)00035-6
OpenAlex ID: W2040492196
description: scientific article; zbMATH DE number 912201