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.

13 pages. Updated for the release of Parts III and IV. All four parts I, II, III, IV are posted on this arXiv

References in corpus (4)

• Subgroup decomposition in Out(F_n), Part I: Geometric Models
• Subgroup decomposition in Out(F_n), Part II: A relative Kolchin theorem
• Subgroup decomposition in $\text{Out}(F_n)$, Part IV: Relatively irreducible subgroups
• Subgroup decomposition in $\text{Out}(F_n)$, Part III: Weak attraction theory

Cited by in corpus (11)

• Boundaries of relative factor graphs and subgroup classification for automorphisms of free products
• Subgroup decomposition in Out(F_n), Part I: Geometric Models
• Subgroup decomposition in Out(F_n), Part II: A relative Kolchin theorem
• Counting loxodromics for hyperbolic actions
• McCool groups of toral relatively hyperbolic groups
• A short proof of Handel and Mosher's alternative for subgroups of $\text{Out}(F_N)$
• Subgroup decomposition in $\text{Out}(F_n)$, Part IV: Relatively irreducible subgroups
• Subgroup decomposition in $\text{Out}(F_n)$, Part III: Weak attraction theory
• Hyperbolic actions and 2nd bounded cohomology of subgroups of $\text{Out}(F_n)$. Part I: Infinite lamination subgroups
• Conical limit points and the Cannon-Thurston map
• Atoroidal dynamics of subgroups of Out(F_N)