Our goal is to find dynamic invariants that completely determine elements of the outer automorphism group Out.Fn) of the free group F n of rank n. To avoid finite order phenomena, we do this for forward rotationless elements. This is not a serious restriction. For example, there is Kn > 0 depending only on n such that, for all φ ε Out.Fn), φKn is forward rotationless. An important part of our analysis is to show that rotationless elements are represented by particularly nice relative train track maps.
All Science Journal Classification (ASJC) codes
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Free group
- Outer automorphisms