The Nielsen-Thurston classification and automorphisms of a free group. I
type: Item
instance of: scholarly article
title: The Nielsen-Thurston classification and automorphisms of a free group. I
zbMATH Open document ID: 0858.20019
DOI: 10.1215/S0012-7094-96-08413-6
published in: Duke Mathematical Journal
publication date: 1997-03-17T00:00:00Z
review text: This is the first of three papers with the same title. In these papers the author constructs a hierarchical decomposition of a given group with respect to a given automorphism of it. This method which sometimes may be considered as a complement to the Bestvina-Handel train tracks and invariant laminations, has already been used, by the author, to obtain the Hopf property for hyperbolic groups (Endomorphisms of hyperbolic groups I, preprint). In the present paper he introduces the basic tools for the construction of the hierarchical decomposition and shows how to obtain the Nielsen-Thurston classification of automorphisms of surfaces on the algebraic level and the Scott conjecture for automorphisms of a free group. The Scott conjecture, already proved in the affirmative by Bestvina and Handel, says that the fixed point subgroup of an automorphism of a free group \(F\) is free of rank not exceeding the rank of \(F\).
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20E05
Mathematics Subject Classification ID: 57M07
zbMATH DE Number: 926952
zbMATH Keywords: train tracks
zbMATH Keywords: invariant laminations
zbMATH Keywords: Hopf property
zbMATH Keywords: hyperbolic groups
zbMATH Keywords: hierarchical decompositions
zbMATH Keywords: Nielsen-Thurston classification
zbMATH Keywords: automorphisms of surfaces
zbMATH Keywords: Scott conjecture
zbMATH Keywords: automorphisms of free groups
zbMATH Keywords: fixed point subgroups
MaRDI profile type: Publication
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author: Zlil Sela
description: scientific article; zbMATH DE number 926952