Mark Feighn

Stable actions of groups on real trees.

This paper further develops Ripss work on real trees. We study a class of actions called ‘stable’ which includes actions with trivial arc stabilizers and small actions of hyperbolic groups.

Laminations, trees, and irreducible automorphisms of free groups

Abstract. We examine the action of Out(Fn) on the set of (irreducible) laminations. Consequences include a special case of the Tits alternative for Out(Fn), the discreteness of certain naturally arising group actions on trees, and word hyperbolicity of certain semidirect products.

The Tits alternative for Out (F~n) I: Dynamics of exponentially-growing automorphisms

The Tits alternative for Out(F_n) is reduced to the case where all elements in the subgroup under consideration grow polynomially.

Bounding the complexity of simplicial group actions on trees

We shall state the main result of this paper in terms of group actions on simplicial trees. Suppose that a group G acts simplicially on a tree T without inversions. For brevity we say that Tis a G-tree. Then the orbit space T/G is a graph whose vertices and edges correspond to G-equivalence classes of vertices and edges in T. Each vertex and edge in T/G is labeled by the stabilizer of a representative of the corresponding equivalence class. This label, a subgroup of G, is well-defined only up to conjugation in G (for details, see [7] or [8]). Thus T/G is a graph of groups whose fundamental group is G. We are interested in finding a number ?(G), depending only on G, so that for every G-tree T, the graph T/G has no more than ?(G) vertices and edges. Some remarks are in order.

Solvable subgroups of Out(Fn) are virtually Abelian

Let Fn be the free group of rank n, let Aut(Fn) be its automorphism group and let Out(Fn) be its outer automorphism group. We show that every solvable subgroup of Out(Fn) has a finite index subgroup that is finitely generated and free Abelian. We also show that every Abelian subgroup of Out(Fn) has a finite index subgroup that lifts to Aut(Fn).

The Recognition Theorem for Out(Fn)

Our goal is to find dynamic invariants that completely determine elements of the outer automorphism group

Abelian subgroups of Out.Fn

\Out(F_n)

A Counterexample to Generalized Accessibility

of the free group

The Grushko decomposition of a finite graph of finite rank free groups: an algorithm

F_n

Hyperbolicity of the complex of free factors

of rank