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S. Gersten announced an algorithm that takes as input two finite sequences $vec K=(K_1,dots, K_N)$ and $vec K=(K_1,dots, K_N)$ of conjugacy classes of finitely generated subgroups of $F_n$ and outputs: (1) $mathsf{YES}$ or $mathsf{NO}$ depending on whether or not there is an element $thetain mathsf{Out}(F_n)$ such that $theta(vec K)=vec K$ together with one such $theta$ if it exists and (2) a finite presentation for the subgroup of $mathsf{Out}(F_n)$ fixing $vec K$. S. Kalajdv{z}ievski published a verification of this algorithm. We present a different algorithm from the point of view of Culler-Vogtmanns Outer space. New results include that the subgroup of $mathsf{Out}(F_n)$ fixing $vec K$ is of type $mathsf{VF}$, an equivariant version of these results, an application, and a unified approach to such questions.
This is the second part of a two part work in which we prove that for every finitely generated subgroup $Gamma < mathsf{Out}(F_n)$, either $Gamma$ is virtually abelian or its second bounded cohomology $H^2_b(Gamma;mathbb{R})$ contains an embedding of
A Kleinian group $Gamma < mathrm{Isom}(mathbb H^3)$ is called convex cocompact if any orbit of $Gamma$ in $mathbb H^3$ is quasiconvex or, equivalently, $Gamma$ acts cocompactly on the convex hull of its limit set in $partial mathbb H^3$. Subgroup sta
This is the fourth and last 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 we develop general ping-pong techniques for the action of $t
In this two part work we prove that for every finitely generated subgroup $Gamma < text{Out}(F_n)$, either $Gamma$ is virtually abelian or $H^2_b(Gamma;mathbb{R})$ contains an embedding of $ell^1$. The method uses actions on hyperbolic spaces, for pu
For any finite collection $f_i$ of fully irreducible automorphisms of the free group $F_n$ we construct a connected $delta$-hyperbolic $Out(F_n)$-complex in which each $f_i$ has positive translation length.