The quadratic isoperimetric inequality for mapping tori of free group automorphisms
نویسندگان
چکیده
منابع مشابه
The Quadratic Isoperimetric Inequality for Mapping Tori of Free Group Automorphisms I: Positive Automorphisms
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 ...
متن کاملThe Quadratic Isoperimetric Inequality for Mapping Tori of Free Group Automorphisms Ii: the General Case
If F is a finitely generated free group and φ is an automorphism of F then F ⋊φZ satisfies a quadratic isoperimetric inequality.
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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...
متن کاملSplittings 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.
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: Memoirs of the American Mathematical Society
سال: 2010
ISSN: 0065-9266,1947-6221
DOI: 10.1090/s0065-9266-09-00578-x