Abstract
Given a free-by-cyclic group determined by any outer automorphism which is represented by an expanding irreducible train-track map , we construct a –complex called the folded mapping torus of , and equip it with a semiflow. We show that 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 containing the homomorphism having , a homology class , and a continuous, convex, homogeneous of degree function with the following properties. Given any primitive integral class there is a graph such that:
The inclusion is –injective and .
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is a section of the semiflow and the first return map to is an expanding irreducible train track map representing such that .
The logarithm of the stretch factor of is precisely .
If was further assumed to be hyperbolic and fully irreducible then for every primitive integral the automorphism of is also hyperbolic and fully irreducible.
Citation
Spencer Dowdall. Ilya Kapovich. Christopher J Leininger. "Dynamics on free-by-cyclic groups." Geom. Topol. 19 (5) 2801 - 2899, 2015. https://doi.org/10.2140/gt.2015.19.2801
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