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.
math.GT↗
arXiv subjects
Michael Handel
Publications and source records attributed to Michael Handel.
Mapping tori of free group automorphisms are coherent
The mapping torus of an endomorphism Φof a group G is the HNN-extension G*_G with bonding maps the identity and Φ. We show that a mapping torus of an injective free group endomorphism has the property that its finitely generated subgroups are finitely presented and, moreover, these subgroups are of finite type.
math.GR↗
The Tits Alternative for $Out(F_n)$ 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 of unipotent automorphisms can be conjugated into an upper-triangular subgroup (this is interpreted via train-tracks).
math.GT↗
Solvable subgroups of Out(F_n) are virtually abelian
A companion result of the the Tits alternative for $Out(F_n)$ is proved: Every solvable subgroup of $Out(F_n)$ is finitely generated and virtually abelian.
math.GT↗