2018/09/07 by Joshua Eike, Eike, Joshua, Abdul Zalloum +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.GR #math.GT
paper · pdf · doi:10.48550/arxiv.1809.02692
openalex publication_date 2018/09/07 · arxiv created 2022/03/21 · arxiv updated 2022/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a finitely generated group. We show that for any finite generating set A, the language consisting of all geodesics in Cay(G,A) with a contracting property is a regular language. As an application, we show that any finitely generated group containing an infinite contracting geodesic must be either virtually ℤ or acylindrically hyperbolic.