Finite-State Machines for Horospheres in Hyperbolic Right-Angled Coxeter Groups
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909758653464576 |
|---|---|
| author | Jillson, Noah Levitin, Daniel N. Saldin, Pramana Stuopis, Katerina Wang, Qianruixi Xue, Kaicheng |
| author_facet | Jillson, Noah Levitin, Daniel N. Saldin, Pramana Stuopis, Katerina Wang, Qianruixi Xue, Kaicheng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18774 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite-State Machines for Horospheres in Hyperbolic Right-Angled Coxeter Groups Jillson, Noah Levitin, Daniel N. Saldin, Pramana Stuopis, Katerina Wang, Qianruixi Xue, Kaicheng Metric Geometry Group Theory 51F30, 20F67, 68Q45 F.1.1 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. |
| title | Finite-State Machines for Horospheres in Hyperbolic Right-Angled Coxeter Groups |
| topic | Metric Geometry Group Theory 51F30, 20F67, 68Q45 F.1.1 |
| url | https://arxiv.org/abs/2406.18774 |