Dynamics on free-by-cyclic groups

@article{Dowdall2015DynamicsOF,
  title={Dynamics on free-by-cyclic groups},
  author={Spencer Dowdall and Ilya Kapovich and Christopher J. Leininger},
  journal={Geometry \& Topology},
  year={2015},
  volume={19},
  pages={2801-2899}
}
Given a free-by-cyclic group GD FN A’ Z determined by any outer automorphism ’2 Out.FN/ which is represented by an expanding irreducible train-track map f , we construct a K.G;1/ 2‐complex X called the folded mapping torus of f , and equip it with a semiflow. We show that X enjoys many similar properties to those proven by Thurston and Fried for the mapping torus of a pseudo-Anosov homeomorphism. In particular, we construct an open, convex cone A H 1 .XIR/D Hom.GIR/ containing the homomorphism… 
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Let 2 Out.Fn/ be a free group outer automorphism that can be represented by an expanding, irreducible train-track map. The automorphism determines a freeby-cyclic group AD Fn A Z and a homomorphism 2
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Consider a group G and an epimorphism u_0:G\to\Z inducing a splitting of G as a semidirect product ker(u_0)\rtimes_\varphi\Z with ker(u_0) a finitely generated free group and \varphi\in Out(ker(u_0))
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