Abstract
We show that if a finitely generated group G has a nonelementary WPD action on a hyperbolic metric space X, then the number of G-conjugacy classes of X-loxodromic elements of G coming from a ball of radius R in the Cayley graph of G grows exponentially in R. As an application we prove that for N ≥ 3 the number of distinct Out(FN)-conjugacy classes of fully irreducible elements Φ from an R-ball in the Cayley graph of Out(FN) with log λ (Φ) of the order of R grows exponentially in R..
Original language | English (US) |
---|---|
Pages (from-to) | 412-421 |
Number of pages | 10 |
Journal | Bulletin of the Australian Mathematical Society |
Volume | 97 |
Issue number | 3 |
DOIs | |
State | Published - Jun 1 2018 |
Keywords
- free group automorphisms
- loxodromic elements
- stretch factors
ASJC Scopus subject areas
- General Mathematics