Subgroup decomposition in Out(F_n): Introduction and Research Announcement

Abstract

This is the introduction to a series of four papers that develop a decomposition theory for subgroups of Out(F_n) which generalizes the theory for elements of Out(F_n) found in the work of Bestvina, Feighn, and Handel on the Tits alternative, and which is analogous to the decomposition theory for subgroups of mapping class groups found in work of Ivanov. In this introduction we state the main theorems and we outline the contents of the whole series.