The Quadratic Isoperimetric Inequality for Mapping Tori of Free Group Automorphisms Ii: the General Case
نویسنده
چکیده
If F is a finitely generated free group and φ is an automorphism of F then F ⋊φZ satisfies a quadratic isoperimetric inequality.
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
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 کاملFree-group Automorphisms, Train Tracks, and the Beaded Decomposition
We study the automorphisms φ of a finitely generated free group F . Building on the train-track technology of Bestvina, Feighn and Handel, we provide a topological representative f : G→ G of a power of φ that behaves very much like the realization on the rose of a positive automorphism. This resemblance is encapsulated in the Beaded Decomposition Theorem which describes the structure of paths i...
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 کاملOn Asymptotic Isoperimetric Constant of Tori
In this note we continue the study of asymptotic invariants of Riemannian tori (e.g. see [BuI] and references there). By asymptotic invariants we mean invariants which do not change under passing to finite covers. In [BuI] we show that the asymptotic volume growth of a Riemannian torus is at least as fast as that of a flat one. One may ask what are the possible values of “asymptotic isoperimetr...
متن کامل