2022/12/26 by Victor Gerasimov, Gerasimov, Victor, Leonid Potyagailo +1 · 1 citation
Computer Science · Mathematics · #20F67 #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Primary 20F65 #Secondary 05C25 #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2212.13199
openalex publication_date 2022/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We establish three criteria of hyperbolicity of a graph in terms of ``average width of geodesic bigons''. In particular we prove that if the ratio of the Van Kampen area of a geodesic bigon β and the length of β in the Cayley graph of a finitely presented group G is bounded above then G is hyperbolic. We plan to use these results to characterize hyperbolic groups in terms of random walks.