The Nielsen-Thurston classification and automorphisms of a free group. I
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 \(F\).
scientific article; zbMATH DE number 926952
scientific article