Counting growth types of automorphisms of free groups
Abstract
Given an automorphism of a free group $F_n$, we consider the following invariants: $e$ is the number of exponential strata (an upper bound for the number of different exponential growth rates of conjugacy classes); $d$ is the maximal degree of polynomial growth of conjugacy classes; $R$ is the rank of the fixed subgroup. We determine precisely which triples $(e,d,R)$ may be realized by an automorphism of $F_n$. In particular, the inequality $e\le (3n2)/4}$ (due to LevittLustig) always holds. In an appendix, we show that any conjugacy class grows like a polynomial times an exponential under iteration of the automorphism.
 Publication:

arXiv eprints
 Pub Date:
 January 2008
 arXiv:
 arXiv:0801.4844
 Bibcode:
 2008arXiv0801.4844L
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Geometric Topology;
 20E05;
 20F65
 EPrint:
 final version, to appear in GAFA