COunting conjugacy classes in out (Fn)

Michael Hull, Ilya Kapovich

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)412-421
Number of pages10
JournalBulletin of the Australian Mathematical Society
Issue number3
StatePublished - Jun 1 2018


  • free group automorphisms
  • loxodromic elements
  • stretch factors

ASJC Scopus subject areas

  • General Mathematics


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