English

Counting Conjugacy Classes in $Out(F_N)$

Group Theory 2017-07-25 v1 Dynamical Systems Geometric Topology

Abstract

We show that if a f.g. group GG has a non-elementary WPD action on a hyperbolic metric space XX, then the number of GG-conjugacy classes of XX-loxodromic elements of GG coming from a ball of radius RR in the Cayley graph of GG grows exponentially in RR. As an application we prove that for N3N\ge 3 the number of distinct Out(FN)Out(F_N)-conjugacy classes of fully irreducibles ϕ\phi from an RR-ball in the Cayley graph of Out(FN)Out(F_N) with logλ(ϕ)\log\lambda(\phi) on the order of RR grows exponentially in RR.

Keywords

Cite

@article{arxiv.1707.07095,
  title  = {Counting Conjugacy Classes in $Out(F_N)$},
  author = {Michael Hull and Ilya Kapovich},
  journal= {arXiv preprint arXiv:1707.07095},
  year   = {2017}
}
R2 v1 2026-06-22T20:54:32.381Z