COunting conjugacy classes in out (Fn)

Michael Hull; Ilya Kapovich

doi:10.1017/S0004972718000047

COunting conjugacy classes in out (F_n)

Michael Hull
, Ilya Kapovich

Mathematics

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.1017/S0004972718000047
State	Published - Jun 1 2018

Keywords

free group automorphisms
loxodromic elements
stretch factors

ASJC Scopus subject areas

General Mathematics

Online availability

10.1017/S0004972718000047

Library availability

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Cite this

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title = "COunting conjugacy classes in out (Fn)",

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..",

keywords = "free group automorphisms, loxodromic elements, stretch factors",

author = "Michael Hull and Ilya Kapovich",

note = "The second author was supported by the individual NSF grants DMS-1405146 and DMS-1710868. Both authors acknowledge the support of the conference grant DMS-1719710 {\textquoteleft}Conference on Groups and Computation{\textquoteright}. {\textcopyright}c 2018 Australian Mathematical Publishing Association Inc.",

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doi = "10.1017/S0004972718000047",

language = "English (US)",

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journal = "Bulletin of the Australian Mathematical Society",

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AU - Hull, Michael

AU - Kapovich, Ilya

N1 - The second author was supported by the individual NSF grants DMS-1405146 and DMS-1710868. Both authors acknowledge the support of the conference grant DMS-1719710 ‘Conference on Groups and Computation’. ©c 2018 Australian Mathematical Publishing Association Inc.

PY - 2018/6/1

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N2 - 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..

AB - 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..

KW - free group automorphisms

KW - loxodromic elements

KW - stretch factors

UR - https://www.scopus.com/pages/publications/85044440868

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