On geodesic ray bundles in hyperbolic groups

Abstract

We construct a Cayley graph ${\mathbf{Cay}}_S(\Gamma )$ of a hyperbolic group $\Gamma$ such that there are elements $g,h\in \Gamma$ and a point $\gamma \in {\partial }_{\infty }\Gamma ={\partial }_{\infty }{\mathbf{Cay}}_S(\Gamma )$ such that the sets $\mathcal{R}\mathcal{B}(g,\gamma )$ and $\mathcal{R}\mathcal{B}(h,\gamma )$ in ${\mathbf{Cay}}_S(\Gamma )$ of vertices along geodesic rays from $g,h$ to $\gamma$ have infinite symmetric difference; thus answering a question of Huang, Sabok and Shinko.

9 pages, 7 figures

References in corpus (1)

• On the one-endedness of graphs of groups

Cited by in corpus (4)

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• Hyperfiniteness of boundary actions of hyperbolic groups
• Unicorn paths and hyperfiniteness for the mapping class group
• On geodesic ray bundles in buildings