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Laminations, trees, and irreducible automorphisms of free groups

- M. Bestvina, M. Feighn, M. Handel
- Mathematics
- 1 May 1997

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… Expand

188 29

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

- M. Bestvina, M. Feighn, M. Handel
- Mathematics
- 3 December 1997

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

183 16- PDF

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 outer… Expand

47 13- PDF

The Tits alternative for Out(Fn) II: A Kolchin type theorem

- M. Bestvina, M. Feighn, M. Handel
- Mathematics
- 3 December 1997

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 of… Expand

138 11- PDF

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.

72 11- PDF

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 this… Expand

47 10- PDF

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

37 8- PDF

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

57 6- PDF

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 outer… Expand

14 5- PDF

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