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arXiv · 2406.18774

Finite-State Machines for Horospheres in Hyperbolic Right-Angled Coxeter Groups

Noah Jillson·Daniel N. Levitin·Pramana Saldin·Katerina Stuopis·Qianruixi Wang·Kaicheng Xue
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Abstract

Relatively little is known about the discrete horospheres in hyperbolic groups, even in simple settings. In this paper we work with hyperbolic one-ended right-angled Coxeter groups and describe two graph structures that mimic the intrinsic metric on a classical horosphere: the Rips graph and the divergence graph (the latter due to Cohen, Goodman-Strauss, and Rieck). We develop, analyze, and implement algorithms based on finite-state machines that draw large finite portions of these graphs, and deduce various geometric corollaries about the path metrics induced by these graph structures.

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Noah Jillson, Daniel N. Levitin, Pramana Saldin, Katerina Stuopis, Qianruixi Wang, Kaicheng Xue. 2024-06-26. Finite-State Machines for Horospheres in Hyperbolic Right-Angled Coxeter Groups. https://doi.org/10.1007/s10711-024-00977-1

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