Mapping Tori of Free Group Automorphisms are Coherent
نویسندگان
چکیده
منابع مشابه
Splittings of mapping tori of free group automorphisms
We present necessary and sufficient conditions for the existence of a splitting over Z of the mapping torus Mφ = F ⋊ Z of a free group automorphism φ, as well as some remarks on the boundary of Mφ in the hyperbolic case.
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If F is a finitely generated free group and φ is a positive automorphism of F then F ⋊φ Z satisfies a quadratic isoperimetric inequality. Associated to an automorphism φ of any group G one has the algebraic mapping torus G ⋊φ Z. In this paper we shall be concerned with the case where G is a finitely generated free group, denoted F . We seek to understand the complexity of word problems for the ...
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We prove that if F is a finitely generated free group and φ is an automorphism of F then F oφ Z satisfies a quadratic isoperimetric inequality. Our proof of this theorem rests on a direct study of the geometry of van Kampen diagrams over the natural presentations of free-by-cylic groups. The main focus of this study is on the dynamics of the time flow of t-corridors, where t is the generator of...
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If F is a finitely generated free group and φ is an automorphism of F then F ⋊φZ satisfies a quadratic isoperimetric inequality.
متن کاملA Remark on Mapping Tori of Free Group Endomorphisms
Proof. It is well-known that the kernels of the powers of φ stabilize (see for example [3]), that is, there exists k > 0 such that ker(φ) = ker(φ) for all n ≥ k. (This easily follows from the stabilization of ranks of the free groups φ(F ) and from Hopficity of finitely generated free groups.) Put N = ker(φ). Then φ factors through to an injective endomorphism φ : F/N → F/N . The group F/N is i...
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ژورنال
عنوان ژورنال: The Annals of Mathematics
سال: 1999
ISSN: 0003-486X
DOI: 10.2307/121081