The automorphism group of the free group of rank 2 is a CAT(0) group
نویسندگان
چکیده
منابع مشابه
The automorphism group of a free-by-cyclic group in rank 2
Let φ be an automorphism of a free group Fn of rank n, and let Mφ = Fn oφ Z be the corresponding mapping torus of φ. We study the group Out(Mφ) under certain technical conditions on φ. Moreover, in the case of rank 2, we classify the cases when this group is finite or virtually cyclic, depending on the conjugacy class of the image of φ in GL2(Z). As an application, we solve the isomorphism prob...
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Let n ≥ 2 and Fn be the free group of rank n. Its automorphism group Aut(Fn) has a well-known surjective linear representation ρ : Aut(Fn) −→ Aut(Fn/F ′ n) = GLn(Z) where F ′ n denotes the commutator subgroup of Fn. By Aut (Fn) := ρ(SLn(Z)) we denote the special automorphism group of Fn. For an epimorphism π : Fn → G of Fn onto a finite group G we call Γ(G, π) := {φ ∈ Aut(Fn) | πφ = π} the stan...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2010
ISSN: 0026-2285
DOI: 10.1307/mmj/1281531457