415 research outputs found
Commensurations of Out(F_n)
Let \Out(F_n) denote the outer automorphism group of the free group
with . We prove that for any finite index subgroup \Gamma<\Out(F_n), the
group \Aut(\Gamma) is isomorphic to the normalizer of in
\Out(F_n). We prove that is {\em co-Hopfian} : every injective
homomorphism is surjective. Finally, we prove that the
abstract commensurator \Comm(\Out(F_n)) is isomorphic to \Out(F_n).Comment: Revised version, 43 pages. To appear in Publ. Math. IHE
Mapping tori of free group automorphisms are coherent
The mapping torus of an endomorphism \Phi of a group G is the HNN-extension
G*_G with bonding maps the identity and \Phi. 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.Comment: 17 pages, published versio
- …