Acylindrically hyperbolic groups and counting problems

2025/04/29 by Inhyeok Choi, Choi, Inhyeok · 1 citation
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2504.20985

openalex publication_date 2025/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that Morse elements are generic in acylindrically hyperbolic groups. As an application, we observe that fully irreducible outer automorphisms are generic in the outer automorphism group of a finite-rank free group.

Citations

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Cited by

• A general construction of simultaneously hyperbolic elements

Related

• Counting pseudo-Anosovs as weakly contracting isometries
• Largest acylindrical actions of free-by-cyclic groups
• Counting problems in graph products and relatively hyperbolic groups
• Small cancellation in acylindrically hyperbolic groups
• A periodicity theorem for acylindrically hyperbolic groups