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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 naturallyExpand
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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.
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Axes in Outer Space
The authors develop a notion of axis in the Culler-Vogtmann outer space $\mathcal{X}_r$ of a finite rank free group $F_r$, with respect to the action of a nongeometric, fully irreducible outerExpand
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The Tits alternative for Out(Fn) II: A Kolchin type theorem
The proof of the Tits alternative for $Out(F_n)$ is completed. The main tool is a Kolchin type theorem, proved in this paper. It states that a finitely generated subgroup of $Out(F_n)$ consisting ofExpand
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The free splitting complex of a free group I: Hyperbolicity
We prove that the free splitting complex of a finite rank free group, also known as Hatcher's sphere complex, is hyperbolic.
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The Recognition Theorem for Out(F_n)
Our goal is to find dynamic invariants that completely determine elements of the outer automorphism group $\Out(F_n)$ of the free group $F_n$ of rank $n$. To avoid finite order phenomena, we do thisExpand
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Subgroup classification in Out(F_n)
For any subgroup H of Out(F_n), either H has a finite index subgroup that fixes the conjugacy class of some proper, nontrivial free factor of F_n, or H contains a fully irreducible element phi,Expand
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Distortion elements in group actions on surfaces
If $\G$ is a finitely generated group with generators $\{g_1,...,g_j\}$ then an infinite order element $f \in \G$ is a {\em distortion element} of $\G$ provided $\displaystyle{\liminf_{n \to \infty}Expand
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Subgroup decomposition in $\text{Out}(F_n)$, Part III: Weak attraction theory
This is the third in a series of four papers (with research announcement posted on this arXiv) that develop a decomposition theory for subgroups of $\text{Out}(F_n)$. In this paper, given an outerExpand
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