The geometry of relative Cayley graphs for subgroups of hyperbolic groups

2002/01/07 by Ilya Kapovich, Kapovich, Ilya · 1 citation
Mathematics · #20F67 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.math/0201045

openalex publication_date 2002/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if H is a quasiconvex subgroup of a hyperbolic group G then the relative Cayley graph Y (also known as the Schreier coset graph) for G/H is Gromov-hyperbolic. We also observe that in this situation if G is torsion-free and non-elementary and H has infinite index in G then the simple random walk on Y is transient.

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