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

被引：0

作者：

Jillson, Noah ^{[1
]}

Levitin, Daniel ^{[1
]}

Saldin, Pramana ^{[1
]}

Stuopis, Katerina ^{[1
]}

Wang, Qianruixi ^{[1
]}

Xue, Kaicheng ^{[1
]}

机构：

[1] Univ Wisconsin Madison, Madison, WI 53703 USA

来源：

GEOMETRIAE DEDICATA | 2025年 / 219卷 / 02期

基金：

美国国家科学基金会;

关键词：

Hyperbolic groups; Right-angled Coxeter groups; Horospheres; Finite-state machines; Algorithms;

D O I：

10.1007/s10711-024-00977-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 (Ergodic Theory and Dynamical Systems 42(9):2740-2783, 2022)). 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.

引用

页数：51

共 22 条

[1] Geodesic growth in right-angled and even Coxeter groups [J].