Geometry & Topology
- Geom. Topol.
- Volume 19, Number 5 (2015), 2801-2899.
Dynamics on free-by-cyclic groups
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 .
- 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.
Geom. Topol., Volume 19, Number 5 (2015), 2801-2899.
Received: 6 June 2014
Revised: 30 December 2014
Accepted: 26 January 2015
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Dowdall, Spencer; Kapovich, Ilya; Leininger, Christopher J. Dynamics on free-by-cyclic groups. Geom. Topol. 19 (2015), no. 5, 2801--2899. doi:10.2140/gt.2015.19.2801. https://projecteuclid.org/euclid.gt/1510858850