Counting growth types of automorphisms of free groups

Details Counting growth types of automorphisms of free groups Counting growth types of automorphisms of free groups

2008-01-31

arxiv.org/abs/0801.4844v2

Mathematics

Group Theory

final version, to appear in GAFA; proof of 3.1 simplified thanks to the referee

Scientific paper

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 $e\le (3n-2)/4}$ (due to Levitt-Lustig) always holds. In an appendix, we show that any conjugacy class grows like a polynomial times an exponential under iteration of the automorphism.

Affiliated with

Also associated with

No associations

Rating

Counting growth types of automorphisms of free groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Counting growth types of automorphisms of free groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Counting growth types of automorphisms of free groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-204212