On geodesic ray bundles in hyperbolic groups

Touikan, Nicholas

doi:10.1090/proc/14117

On geodesic ray bundles in hyperbolic groups
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by Nicholas Touikan

Proc. Amer. Math. Soc. 146 (2018), 4165-4173

DOI: https://doi.org/10.1090/proc/14117

Published electronically: July 5, 2018

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Abstract:

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

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